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Find link is a tool written by Edward Betts.Longer titles found: Bijection, injection and surjection (view)
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alternate case: bijection
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is that no bijection can exist between {1, 2, ..., n} and {1, 2, ..., m} unless n = m; this fact (together with the fact that two bijections can be composedDedekind-infinite set (1,751 words) [view diff] exact match in snippet view article find links to article
set is Dedekind-finite if it is not Dedekind-infinite (i.e., no such bijection exists). Proposed by Dedekind in 1888, Dedekind-infiniteness was the firstBijective proof (400 words) [view diff] exact match in snippet view article find links to article
other sets that are easier to count. Additionally, the nature of the bijection itself often provides powerful insights into each or both of the setsTheorem of the highest weight (1,103 words) [view diff] exact match in snippet view article find links to article
compact Lie group K {\displaystyle K} . The theorem states that there is a bijection λ ↦ [ V λ ] {\displaystyle \lambda \mapsto [V^{\lambda }]} from the setMultiplicative inverse (2,360 words) [view diff] exact match in snippet view article find links to article
(for example in French, the inverse function is preferably called the bijection réciproque). In the real numbers, zero does not have a reciprocal (divisionEilenberg–MacLane space (3,357 words) [view diff] exact match in snippet view article find links to article
based maps from X to K ( G , n ) {\displaystyle K(G,n)} is in natural bijection with the n-th singular cohomology group H n ( X , G ) {\displaystyle H^{n}(XHume's principle (820 words) [view diff] exact match in snippet view article find links to article
correspondence (a bijection) between F {\displaystyle {\mathcal {F}}} and G {\displaystyle {\mathcal {G}}} . In other words, that bijections are the "correct"Locally constant sheaf (537 words) [view diff] exact match in snippet view article find links to article
path p : [ 0 , 1 ] → X {\displaystyle p:[0,1]\to X} in X determines a bijection F p ( 0 ) → ∼ F p ( 1 ) . {\displaystyle {\mathcal {F}}_{p(0)}{\oversetNew digraph reconstruction conjecture (735 words) [view diff] exact match in snippet view article find links to article
follows: If G and H are two graphs on at least three vertices and ƒ is a bijection from V(G) to V(H) such that G\{v} and H\{ƒ(v)} are isomorphic for allLee distance (729 words) [view diff] exact match in snippet view article find links to article
bigger than 1. However, there exists a Gray isometry (weight-preserving bijection) between Z 4 {\displaystyle \mathbb {Z} _{4}} with the Lee weight andCrossover effects (1,863 words) [view diff] exact match in snippet view article find links to article
attribute the judgements on coreference with respect to weak crossover to the Bijection Principle: “There is a bijective correspondence between variables andCritical point (set theory) (341 words) [view diff] exact match in snippet view article
\{A\mid A\subseteq \kappa \land \kappa \in j(A)\}} , which defines a bijection between elementary embeddings and ultrafilters. Generally, there willHartogs number (690 words) [view diff] exact match in snippet view article find links to article
e. ordinal) not less than or equal to the cardinality of X (with the bijection definition of cardinality and the injective function order). (If we restrictClass field theory (2,203 words) [view diff] exact match in snippet view article find links to article
existence theorem states that the reciprocity map can be used to give a bijection between the set of abelian extensions of F and the set of closed subgroupsMyhill isomorphism theorem (1,122 words) [view diff] exact match in snippet view article find links to article
this does not work since the constructed bijection need not be computable. Instead, we build the bijection by successively pairing elements. At eachComputable isomorphism (180 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mu } are called computably isomorphic if there exists a computable bijection f {\displaystyle f} so that ν = μ ∘ f {\displaystyle \nu =\mu \circ f}Skew lattice (5,159 words) [view diff] exact match in snippet view article find links to article
skew lattice is categorical if nonempty composites of coset bijections are coset bijections. Categorical skew lattices form a variety. Skew lattices inClosed-subgroup theorem (2,905 words) [view diff] exact match in snippet view article find links to article
τr) is not a Lie group. While the map exp : h → (H, τr) is an analytic bijection, its inverse is not continuous. That is, if U ⊂ h corresponds to a smallFredholm alternative (1,464 words) [view diff] exact match in snippet view article find links to article
K − λ : X → X is a bijection ⇔ (K − λ) (L + μ0) = Id − λ (L + μ0) : dom(L) → X is a bijection ⇔ L + μ0 − λ−1 : dom(L) → X is a bijection. Replacing -μ0+λ−1Honda–Tate theorem (203 words) [view diff] exact match in snippet view article find links to article
Taira Honda (1968) showed that this map is surjective, and therefore a bijection. Honda, Taira (1968), "Isogeny classes of abelian varieties over finitePrimary cyclic group (216 words) [view diff] exact match in snippet view article find links to article
_{{p_{i}}^{m_{i}}}.} This expression is essentially unique: there is a bijection between the sets of groups in two such expressions, which maps each groupLegendrian knot (361 words) [view diff] exact match in snippet view article find links to article
classes of Legendrian knots modulo negative Legendrian stabilizations is in bijection with the set of transverse knots. Geiges, Hansjörg (2008). An introductionGroup algebra of a locally compact group (1,339 words) [view diff] exact match in snippet view article find links to article
bijection between the set of strongly continuous unitary representations of G and non-degenerate bounded *-representations of Cc(G). This bijection respectsDensity theorem (category theory) (798 words) [view diff] exact match in snippet view article
there is a natural bijection G ( U ) ≃ Hom ( h U , G ) {\displaystyle G(U)\simeq \operatorname {Hom} (h_{U},G)} . Under this bijection, α U , x {\displaystyleBianchi group (456 words) [view diff] exact match in snippet view article find links to article
({\sqrt {-d}})}(2)\ .} The set of cusps of M d {\displaystyle M_{d}} is in bijection with the class group of Q ( − d ) {\displaystyle \mathbb {Q} ({\sqrt {-d}})}Carleman's condition (379 words) [view diff] exact match in snippet view article find links to article
demonstrated by a counter-example. In fact, the example violates the bijection, i.e. determinacy, property in the probability sum theorem. When the integrandDescriptive set theory (1,590 words) [view diff] exact match in snippet view article find links to article
Baire space; in fact every Polish space is the image of a continuous bijection defined on a closed subset of Baire space. Similarly, every compact PolishList of things named after James Joseph Sylvester (517 words) [view diff] exact match in snippet view article find links to article
n × p matrix B. Sylver coinage, a number-theoretic game. Sylvester's bijection, a correspondence between partitions into distinct and odd parts. SylvesterList of things named after James Joseph Sylvester (517 words) [view diff] exact match in snippet view article find links to article
n × p matrix B. Sylver coinage, a number-theoretic game. Sylvester's bijection, a correspondence between partitions into distinct and odd parts. SylvesterMyhill–Nerode theorem (1,178 words) [view diff] exact match in snippet view article find links to article
this gives us a bijection between states of A {\displaystyle A} and the states of the canonical acceptor. It is clear that this bijection also preservesSpin structure (4,373 words) [view diff] exact match in snippet view article find links to article
P_{E}} are in bijection with index 2 {\displaystyle 2} subgroups of π 1 ( P E ) {\displaystyle \pi _{1}(P_{E})} , which is in bijection with the set ofAssociated prime (979 words) [view diff] exact match in snippet view article find links to article
\mathrm {Spec} (R).} If R is an Artinian ring, then this map becomes a bijection. Matlis' Theorem: For a commutative Noetherian ring R, the map from theOperator (linguistics) (613 words) [view diff] exact match in snippet view article
Theory. Blackwell. Koopman, H., & Sportiche, D. (1982). Variables and the Bijection Principle. The Linguistic Review, 2, 139-60. Cinque, Guglielmo (1991)Cobordism hypothesis (412 words) [view diff] exact match in snippet view article find links to article
adjointable, for 1 ≤ k ≤ n − 1 {\displaystyle 1\leq k\leq n-1} , there is a bijection between the C {\displaystyle {\mathcal {C}}} -valued symmetric monoidalMatrix ring (1,812 words) [view diff] exact match in snippet view article find links to article
construction, the left ideals of Mn(C) are in bijection with the subspaces of Cn. There is a bijection between the two-sided ideals of Mn(R) and the two-sidedYoneda lemma (3,448 words) [view diff] exact match in snippet view article find links to article
of F ( A ) {\displaystyle F(A)} ; rather intuitively, there exists a bijection between H o m ( H o m ( A , − ) , F ) {\displaystyle \mathrm {Hom} (\mathrmCombinatorial number system (1,871 words) [view diff] exact match in snippet view article find links to article
the k-combinations taken from N; in this view the correspondence is a bijection. The number N corresponding to (ck, ..., c2, c1) is given by N = ( c kOpen mapping theorem (functional analysis) (3,954 words) [view diff] exact match in snippet view article
the second lemma. ◻ {\displaystyle \square } In general, a continuous bijection between topological spaces is not necessarily a homeomorphism. The openZonohedron (2,522 words) [view diff] exact match in snippet view article find links to article
{\mathcal {M}}} represented by M {\displaystyle {M}} , then we obtain a bijection between facets of Z {\displaystyle Z} and signed cocircuits of M {\displaystyleElementary class (1,281 words) [view diff] exact match in snippet view article find links to article
for which these two subsets have the same cardinality, i.e., there is a bijection between them. This class is not elementary, because a σ-structure in whichLagrange's theorem (group theory) (2,250 words) [view diff] exact match in snippet view article
cardinality as H because x ↦ a x {\displaystyle x\mapsto ax} defines a bijection H → a H {\displaystyle H\to aH} (the inverse is y ↦ a − 1 y {\displaystyleMoving frame (2,587 words) [view diff] exact match in snippet view article find links to article
This mapping determined by the frame ƒ is a bijection from the points of X to those of Σ. This bijection is compatible with the law of composition ofMoving frame (2,587 words) [view diff] exact match in snippet view article find links to article
This mapping determined by the frame ƒ is a bijection from the points of X to those of Σ. This bijection is compatible with the law of composition ofSchlessinger's theorem (608 words) [view diff] exact match in snippet view article find links to article
extension in C and Y→X is some morphism in C. H2: The map in H1 is a bijection whenever Z→X is the small extension k[x]/(x2)→k. H3: The tangent spaceModular representation theory (2,613 words) [view diff] exact match in snippet view article find links to article
p, there is a bijection between roots of unity in K and complex roots of unity of order coprime to p. Once a choice of such a bijection is fixed, theJBoss Seam (447 words) [view diff] exact match in snippet view article find links to article
incorporates identity management features. Seam 2 introduces the concept of bijection, taken from Spring's dependency injection feature, where objects can beConservative functor (131 words) [view diff] exact match in snippet view article find links to article
functor from Top to Set is not conservative because not every continuous bijection is a homeomorphism. Every faithful functor from a balanced category isShannon number (626 words) [view diff] exact match in snippet view article find links to article
(4.822\pm 0.028)\times 10^{44}} , based on an efficiently computable bijection between integers and chess positions. As a comparison to the Shannon numberPushforward measure (1,103 words) [view diff] exact match in snippet view article find links to article
measure to the interval [0, 2π) and let f : [0, 2π) → S1 be the natural bijection defined by f(t) = exp(i t). The natural "Lebesgue measure" on S1 is thenGalois representation (1,927 words) [view diff] exact match in snippet view article find links to article
GK. For example, via rK the continuous complex characters of WK are in bijection with those of CK. Thus, the absolute value character on CK yields a character2-bridge knot (308 words) [view diff] exact match in snippet view article find links to article
numerator closures of rational tangles. This definition can be used to give a bijection between the set of 2-bridge links and the set of rational numbers; theBasis (universal algebra) (2,000 words) [view diff] exact match in snippet view article
the inner condition b is a basis, when ϱ {\displaystyle \varrho } is a bijection from E onto the set of all m, namely for each m there is one and onlyPartial trace (2,121 words) [view diff] exact match in snippet view article find links to article
sets and bijections between them, in which the monoidal product is disjoint union. One can show that for any finite sets, X,Y,U and bijection X + U ≅ YCombinatorial mirror symmetry (845 words) [view diff] exact match in snippet view article find links to article
octahedron, the dodecahedron is dual to icosahedron. There is a natural bijection between the k {\displaystyle k} -dimensional faces of a d {\displaystyleLai–Massey scheme (910 words) [view diff] exact match in snippet view article find links to article
\sigma (x)-x} are permutations (in the mathematical sense, that is, a bijection – not a permutation box). Since there are no orthomorphisms for bit blocksDerivative of the exponential map (5,286 words) [view diff] exact match in snippet view article find links to article
that exp is a bi-analytic bijection in a neighborhood of 0 ∈ g in matrix space. Furthermore, exp, is a bi-analytic bijection from a neighborhood of 0 ∈Conformal radius (1,453 words) [view diff] exact match in snippet view article find links to article
that it behaves well under conformal maps: if φ : D → D′ is a conformal bijection and z in D, then rad ( φ ( z ) , D ′ ) = | φ ′ ( z ) | rad ( z , DWilhelm Ackermann (425 words) [view diff] exact match in snippet view article find links to article
life. He died in Lüdenscheid, West Germany in December 1962. Ackermann's bijection Ackermann coding Ackermann function Ackermann ordinal Ackermann set theoryTopos (4,308 words) [view diff] exact match in snippet view article find links to article
pullback of t along f: X → Ω is a monic. The monics to X are therefore in bijection with the pullbacks of t along morphisms from X to Ω. The latter morphismsRiesz representation theorem (12,630 words) [view diff] exact match in snippet view article find links to article
The inverse of any antilinear (resp. linear) bijection is again an antilinear (resp. linear) bijection. The composition of two antilinear maps is a linearTopos (4,308 words) [view diff] exact match in snippet view article find links to article
pullback of t along f: X → Ω is a monic. The monics to X are therefore in bijection with the pullbacks of t along morphisms from X to Ω. The latter morphismsMöbius function (3,124 words) [view diff] exact match in snippet view article find links to article
n=1} . Suppose then that n > 1 {\displaystyle n>1} . Then there is a bijection between the factors d {\displaystyle d} of n {\displaystyle n} for which*-autonomous category (912 words) [view diff] exact match in snippet view article find links to article
}:A\to (A\Rightarrow \bot )\Rightarrow \bot } defined as the image by the bijection defining the monoidal closure H o m ( ( A ⇒ ⊥ ) ⊗ A , ⊥ ) ≅ H o m ( AEquivariant cohomology (1,813 words) [view diff] exact match in snippet view article find links to article
In the non-equivariant case, the first Chern class can be viewed as a bijection between the set of all isomorphism classes of complex line bundles onNear-field (mathematics) (1,767 words) [view diff] exact match in snippet view article
ϕ : M → A ∖ { 0 } {\displaystyle \phi :M\to A\setminus \{0\}} be the bijection m ↦ 1 ∗ m {\displaystyle m\mapsto 1\ast m} . Then we define addition onUnit (ring theory) (1,526 words) [view diff] exact match in snippet view article
group ring construction). Explicitly this means that there is a natural bijection between the set of the ring homomorphisms Z [ t , t − 1 ] → R {\displaystyleSupercompact cardinal (886 words) [view diff] exact match in snippet view article find links to article
holds below κ {\displaystyle \kappa } then it holds everywhere because a bijection between the powerset of ν {\displaystyle \nu } and a cardinal at leastCore (graph theory) (399 words) [view diff] exact match in snippet view article
f : C → C {\displaystyle f:C\to C} is an isomorphism, that is it is a bijection of vertices of C {\displaystyle C} . A core of a graph G {\displaystyleBorel subgroup (948 words) [view diff] exact match in snippet view article find links to article
algebraic group G, the set of conjugacy classes of parabolic subgroups is in bijection with the set of all subsets of nodes of the corresponding Dynkin diagram;Pentagonal number theorem (2,118 words) [view diff] exact match in snippet view article find links to article
all partitions of n {\displaystyle n} . All that remains is to give a bijection from one set to the other, which is accomplished by the function φ fromHook length formula (5,141 words) [view diff] exact match in snippet view article find links to article
at each step there are never more preceding D's than U's. These are in bijection with the Young tableaux of shape λ = ( n , n ) {\displaystyle \lambdaLimit set (1,114 words) [view diff] exact match in snippet view article find links to article
} If f {\displaystyle f} is a homeomorphism (that is, a bicontinuous bijection), then the α {\displaystyle \alpha } -limit set is defined in a similarNuclear operator (4,791 words) [view diff] exact match in snippet view article find links to article
{\displaystyle L_{0}\left(x+\ker L\right):=L(x)} defines a bijection called the canonical bijection associated with L. X* or X ′ {\displaystyle X'} will denoteHomotopy extension property (615 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\tilde {f}}_{\bullet }\colon X\to Y^{I}} are in natural bijection with expressions as maps f ~ ∙ : X × I → Y {\displaystyle {\tilde {f}}_{\bulletRose (topology) (496 words) [view diff] exact match in snippet view article
many petals is similar to the Hawaiian earring: there is a continuous bijection from this rose onto the Hawaiian earring, but the two are not homeomorphicSystem of imprimitivity (3,055 words) [view diff] exact match in snippet view article find links to article
Suppose G acts on X transitively with quasi-invariant measure μ. There is a bijection from unitary equivalence classes of systems of imprimitivity of (G, X)Fundamental theorem of Galois theory (3,001 words) [view diff] exact match in snippet view article find links to article
separable. The problem that one encounters in the infinite case is that the bijection in the fundamental theorem does not hold as we get too many subgroupsAtkinson's theorem (618 words) [view diff] exact match in snippet view article find links to article
}\oplus \operatorname {Ker} (T).} The restriction T : Ker(T)⊥ → Ran(T) is a bijection, and therefore invertible by the open mapping theorem. Extend this inverseFundamental theorem of Galois theory (3,001 words) [view diff] exact match in snippet view article find links to article
separable. The problem that one encounters in the infinite case is that the bijection in the fundamental theorem does not hold as we get too many subgroupsAtkinson's theorem (618 words) [view diff] exact match in snippet view article find links to article
}\oplus \operatorname {Ker} (T).} The restriction T : Ker(T)⊥ → Ran(T) is a bijection, and therefore invertible by the open mapping theorem. Extend this inverseAffine variety (4,377 words) [view diff] exact match in snippet view article find links to article
correspondence between affine algebraic sets and radical ideals is a bijection. The coordinate ring of an affine algebraic set is reduced (nilpotent-free)Model transformation (944 words) [view diff] exact match in snippet view article find links to article
models is consistent if and only if it is related by the consistency bijection. Both models contain the same information, but presented differently.Penrose transform (974 words) [view diff] exact match in snippet view article find links to article
projections. Using spinor index notation, the Penrose transform gives a bijection between solutions to the spin ± n / 2 {\displaystyle \pm n/2} masslessCatalan number (6,013 words) [view diff] exact match in snippet view article find links to article
because the reflection process is reversible, the reflection is therefore a bijection between bad paths in the original grid and monotonic paths in the newLefschetz theorem on (1,1)-classes (778 words) [view diff] exact match in snippet view article
case where X is a projective variety, holomorphic line bundles are in bijection with linear equivalences class of divisors, and given a divisor D on XBinary tree (5,097 words) [view diff] exact match in snippet view article find links to article
same way. Instead, they are related by the following recursively defined bijection: the Dyck word equal to the empty string corresponds to the binary treeBanach space (17,049 words) [view diff] exact match in snippet view article find links to article
normed spaces, they are isomorphic normed spaces if there exists a linear bijection T : X → Y {\displaystyle T:X\to Y} such that T {\displaystyle T} and itsSize (1,715 words) [view diff] exact match in snippet view article find links to article
assign to each suitable subset a number cardinality (equal if there is a bijection), of a set is a measure of the "number of elements of the set" for well-orderedIntegral of inverse functions (1,696 words) [view diff] exact match in snippet view article find links to article
{\displaystyle f^{-1}} are Riemann integrable and the identity follows from a bijection between lower/upper Darboux sums of f {\displaystyle f} and upper/lowerKuratowski closure axioms (3,812 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \mathbf {c} \mapsto {\mathfrak {S}}[\mathbf {c} ]} is a bijection, whose inverse is given by the assignment C : κ ↦ c κ {\displaystyle {\mathfrakAbsolute convergence (5,193 words) [view diff] exact match in snippet view article find links to article
{\textstyle \sum _{x\in X}f(x)} only in the case where there exists some bijection g : Z + → X {\displaystyle g:\mathbb {Z} ^{+}\to X} such that ∑ n = 1Tautological bundle (2,440 words) [view diff] exact match in snippet view article find links to article
universal bundle in the sense: for each compact space X, there is a natural bijection { [ X , G n ] → Vect n R ( X ) f ↦ f ∗ ( γ n ) {\displaystyle {\begin{cases}[XCohomology (7,049 words) [view diff] exact match in snippet view article find links to article
{\displaystyle X\to K(A,j)} . More precisely, pulling back the class u gives a bijection [ X , K ( A , j ) ] → ≅ H j ( X , A ) {\displaystyle [X,K(A,j)]{\stackrelRoot datum (543 words) [view diff] exact match in snippet view article find links to article
}} is a finite subset of X ∗ {\displaystyle X_{\ast }} and there is a bijection from Φ {\displaystyle \Phi } onto Φ ∨ {\displaystyle \Phi ^{\vee }} ,Rational number (3,397 words) [view diff] exact match in snippet view article find links to article
sequence that contains each rational number exactly once. This establishes a bijection between the rational numbers and the natural numbers, which maps eachA¹ homotopy theory (2,762 words) [view diff] exact match in snippet view article find links to article
0 : { 0 } → A 1 {\displaystyle i_{0}:\{0\}\to \mathbb {A} ^{1}} is a bijection. Here we are considering A 1 {\displaystyle \mathbb {A} ^{1}} as a sheafInfrastructure (number theory) (2,490 words) [view diff] exact match in snippet view article
_{fRep}:fRep\to \mathbb {R} /R\mathbb {Z} ,\;(x,f)\mapsto d(x)+f} is a bijection and that ( x , 0 ) ∈ f R e p {\displaystyle (x,0)\in fRep} for every xMorphism of schemes (5,034 words) [view diff] exact match in snippet view article find links to article
stated as follows: for any scheme X and a ring A, there is a natural bijection: Mor ( X , Spec ( A ) ) ≅ Hom ( A , Γ ( X , O X ) ) . {\displaystyleSchur polynomial (3,773 words) [view diff] exact match in snippet view article find links to article
the Robinson–Schensted–Knuth correspondence are examples of such bijections. A bijection with more structure is a proof using so called crystals. This methodHereditary C*-subalgebra (559 words) [view diff] exact match in snippet view article find links to article
C*-subalgebra. In fact, L* ∩ L is hereditary and the map L ↦ L* ∩ L is a bijection. It follows from this correspondence that every closed ideal is a hereditaryHereditary C*-subalgebra (559 words) [view diff] exact match in snippet view article find links to article
C*-subalgebra. In fact, L* ∩ L is hereditary and the map L ↦ L* ∩ L is a bijection. It follows from this correspondence that every closed ideal is a hereditaryStein factorization (427 words) [view diff] exact match in snippet view article find links to article
connected components of the fiber f − 1 ( s ) {\displaystyle f^{-1}(s)} is in bijection with the set of points in the fiber g − 1 ( s ) {\displaystyle g^{-1}(s)}Representable functor (1,893 words) [view diff] exact match in snippet view article find links to article
{Hom} _{\mathcal {D}}(FX,Y)\to \mathrm {Hom} _{\mathcal {C}}(X,GY)} is a bijection for all X and Y. The dual statements are also true. Let F : C → D be aSubcountability (3,589 words) [view diff] exact match in snippet view article find links to article
functions X → { 0 , 1 } {\displaystyle X\to \{0,1\}} are not automatically in bijection with all the subsets of X {\displaystyle X} . So constructively, subsetsSemisimple Lie algebra (5,743 words) [view diff] exact match in snippet view article find links to article
having the same highest weight are equivalent. In short, there exists a bijection between h ∗ {\displaystyle {\mathfrak {h}}^{*}} and the set of the equivalenceNormal subgroup (3,156 words) [view diff] exact match in snippet view article find links to article
f} (the first isomorphism theorem). In fact, this correspondence is a bijection between the set of all quotient groups of G , G / N , {\displaystyle GBanach algebra (2,618 words) [view diff] exact match in snippet view article find links to article
field, and it follows from the Gelfand–Mazur theorem that there is a bijection between the set of all maximal ideals of A {\displaystyle A} and the setGrothendieck topology (4,507 words) [view diff] exact match in snippet view article find links to article
X), F) → Hom(S, F), induced by the inclusion of S into Hom(−, X), is a bijection. Halfway in between a presheaf and a sheaf is the notion of a separatedGelfand representation (1,815 words) [view diff] exact match in snippet view article find links to article
the case where A {\displaystyle A} has an identity element, there is a bijection between Φ A {\displaystyle \Phi _{A}} and the set of maximal ideals inDuality (projective geometry) (5,688 words) [view diff] exact match in snippet view article
over the opposite skewfield Ko. There is thus an inclusion-reversing bijection between the projective spaces PG(n, K) and PG(n, Ko). If K and Ko areFree object (2,027 words) [view diff] exact match in snippet view article find links to article
functor is a left adjoint to the faithful functor U; that is, there is a bijection Hom S e t ( X , U ( B ) ) ≅ Hom C ( F ( X ) , B ) . {\displaystyleDoob–Dynkin lemma (566 words) [view diff] exact match in snippet view article find links to article
{\displaystyle S} is bijective with [ 0 , 1 ] , {\displaystyle [0,1],} and the bijection is measurable in both directions. By definition, the measurability ofClosed monoidal category (1,167 words) [view diff] exact match in snippet view article find links to article
{\displaystyle A\mapsto (B\Rightarrow A).} This means that there exists a bijection, called 'currying', between the Hom-sets Hom C ( A ⊗ B , C ) ≅ Hom C (Hilbert's paradox of the Grand Hotel (2,131 words) [view diff] exact match in snippet view article find links to article
set of natural numbers since the rationals are countable: there is a bijection from the naturals to the rationals. List of paradoxes – List of statementsBernhard Riemann (2,926 words) [view diff] exact match in snippet view article find links to article
the complex plane is "biholomorphically equivalent" (i.e. there is a bijection between them that is holomorphic with a holomorphic inverse) to eitherAx–Grothendieck theorem (920 words) [view diff] exact match in snippet view article find links to article
function as a polynomial: any injection of a finite set to itself is a bijection. When F {\displaystyle F} is the algebraic closure of a finite field,Ordered field (2,208 words) [view diff] exact match in snippet view article find links to article
maximal preorderings. Let F {\displaystyle F} be a field. There is a bijection between the field orderings of F {\displaystyle F} and the positive conesParabolic Lie algebra (400 words) [view diff] exact match in snippet view article find links to article
algebra g {\displaystyle {\mathfrak {g}}} , parabolic subalgebras are in bijection with subsets of simple roots, i.e. subsets of the nodes of the DynkinParabolic Lie algebra (400 words) [view diff] exact match in snippet view article find links to article
algebra g {\displaystyle {\mathfrak {g}}} , parabolic subalgebras are in bijection with subsets of simple roots, i.e. subsets of the nodes of the DynkinOrbit method (839 words) [view diff] exact match in snippet view article find links to article
lattice of G. The highest weight theory can be restated in the form of a bijection between the set of integral coadjoint orbits and the set of equivalenceNumber line (2,549 words) [view diff] exact match in snippet view article find links to article
The bijection between points on the real line and vectorsOrdered field (2,208 words) [view diff] exact match in snippet view article find links to article
maximal preorderings. Let F {\displaystyle F} be a field. There is a bijection between the field orderings of F {\displaystyle F} and the positive conesKoecher–Vinberg theorem (361 words) [view diff] exact match in snippet view article find links to article
transformation T : A → A {\displaystyle T\colon A\to A} that restricts to a bijection C → C {\displaystyle C\to C} and satisfies T ( a ) = b {\displaystyleNormal invariant (2,386 words) [view diff] exact match in snippet view article find links to article
obtains an (unnatural) bijection N ( X ) ≅ [ X , G / O ] . {\displaystyle {\mathcal {N}}(X)\cong [X,G/O].} The above bijection gives N ( X ) {\displaystyleMarcel-Paul Schützenberger (1,277 words) [view diff] exact match in snippet view article find links to article
1016/S0001-8708(02)00038-5. Lam, Thomas; Shimozono, Mark (2006). "A Little Bijection for Affine Stanley Symmetric Functions" (PDF). Séminaire LotharingienWeil group (984 words) [view diff] exact match in snippet view article find links to article
correspondence for GLn over K (now proved) states that there is a natural bijection between isomorphism classes of irreducible admissible representationsFueter–Pólya theorem (614 words) [view diff] exact match in snippet view article find links to article
variables whose restriction to N 2 {\displaystyle \mathbb {N} ^{2}} is a bijection from N 2 {\displaystyle \mathbb {N} ^{2}} to N {\displaystyle \mathbbLossless compression (4,155 words) [view diff] exact match in snippet view article find links to article
"plain" to "compressed" bit sequences. The pigeonhole principle prohibits a bijection between the collection of sequences of length N and any subset of theProjective variety (7,499 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \alpha _{i}=f^{*}(u_{i})\in L.} For each L, the construction is a bijection between the set of L-points of P ˘ k n {\displaystyle {\breve {\mathbbGlossary of Principia Mathematica (1,102 words) [view diff] exact match in snippet view article find links to article
complete totally ordered set isomorphic to the reals. *275 correlator bijection couple 1. A cardinal couple is a class with exactly two elements 2. AnCardinality of the continuum (2,381 words) [view diff] exact match in snippet view article find links to article
b ∈ R {\displaystyle a,b\in \mathbb {R} } . We therefore define the bijection f : R 2 → C ( a , b ) ↦ a + b i {\displaystyle {\begin{aligned}f\colonOper (mathematics) (890 words) [view diff] exact match in snippet view article
{\displaystyle ^{L}{\mathfrak {g}}} as the Langlands dual algebra, there is a bijection between the spectrum of the Gaudin algebra generated by operators definedGlossary of Principia Mathematica (1,102 words) [view diff] exact match in snippet view article find links to article
complete totally ordered set isomorphic to the reals. *275 correlator bijection couple 1. A cardinal couple is a class with exactly two elements 2. AnIndex of a subgroup (2,612 words) [view diff] exact match in snippet view article find links to article
{\displaystyle 1\in \mathbf {Z} /p,} which shows that this map is a bijection. As a consequence, the number of normal subgroups of index p is ( p kOrthonormal basis (2,707 words) [view diff] exact match in snippet view article find links to article
_{i=1}^{n}v^{i}e_{i}.} These definitions make it manifest that there is a bijection { Space of orthogonal bases B } ↔ { Space of isomorphisms V ↔ R n }Sierpiński space (1,913 words) [view diff] exact match in snippet view article find links to article
topology of X (that is, the family of all open sets). Then we have a bijection from T ( X ) {\displaystyle T(X)} to C ( X , S ) {\displaystyle C(X,S)}Plancherel measure (1,168 words) [view diff] exact match in snippet view article find links to article
{\displaystyle S_{n}^{\wedge }} of irreducible representations is in natural bijection with the set of integer partitions of n {\displaystyle n} . For an irreducibleSchubert polynomial (1,509 words) [view diff] exact match in snippet view article find links to article
certain combinatorial objects called pipe dreams or rc-graphs. These are in bijection with reduced Kogan faces, (introduced in the PhD thesis of Mikhail Kogan)Lafforgue's theorem (709 words) [view diff] exact match in snippet view article find links to article
some prime not equal to p. Lafforgue's theorem states that there is a bijection σ between: Equivalence classes of cuspidal representations π of GLn(F)Category of elements (2,842 words) [view diff] exact match in snippet view article find links to article
to a canonical bijection, as for each i ∈ I , A i ≅ π − 1 ( { i } ) {\displaystyle i\in I,A_{i}\cong \pi ^{-1}(\{i\})} via the bijection a ↦ ( i , a )Antilinear map (1,765 words) [view diff] exact match in snippet view article find links to article
{\overline {X}}^{\prime }.} This says exactly that the canonical antilinear bijection defined by Cong : X ′ → X ¯ ′ where Cong ( f ) := f ¯ {\displaystyleTuring degree (3,130 words) [view diff] exact match in snippet view article find links to article
These requirements are put into a priority ordering, which is an explicit bijection of the requirements and the natural numbers. The proof proceeds inductivelyCreative and productive sets (1,306 words) [view diff] exact match in snippet view article find links to article
is recursively isomorphic to K, that is, there is a total computable bijection f on the natural numbers such that f(C) = K. The set of all provable sentencesCoarse structure (1,327 words) [view diff] exact match in snippet view article find links to article
this structure, a map is a coarse equivalence if and only if it is a bijection (of sets). The C 0 {\displaystyle C_{0}} coarse structure on a metricFrame bundle (3,035 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \phi _{i,x}:E_{x}\to \mathbb {R} ^{k}} . This data determines a bijection ψ i : π − 1 ( U i ) → U i × G L ( k , R ) {\displaystyle \psi _{i}:\piFlow (mathematics) (2,703 words) [view diff] exact match in snippet view article
the mapping φ t : X → X {\displaystyle \varphi ^{t}:X\to X} is a bijection with inverse φ − t : X → X . {\displaystyle \varphi ^{-t}:X\to X.} Quotient space of an algebraic stack (232 words) [view diff] exact match in snippet view article find links to article
coarse moduli requires a universality.) In other words, there is a natural bijection between the set of all open immersions to F and the set of all open subsetsConnection (principal bundle) (3,436 words) [view diff] exact match in snippet view article
is the dual lie algebra, hence G {\displaystyle G} -connections are in bijection with C ∞ ( H , g ∗ ⊗ g ) G {\displaystyle C^{\infty }(H,{\mathfrak {g}}^{*}\otimesQ-Pochhammer symbol (2,654 words) [view diff] exact match in snippet view article find links to article
arbitrary partition with at most n parts. This gives a weight-preserving bijection between the set of partitions into n or n − 1 distinct parts and the setCompact space (5,704 words) [view diff] exact match in snippet view article find links to article
disjoint open sets U and V in X such that A ⊆ U and B ⊆ V. A continuous bijection from a compact space into a Hausdorff space is a homeomorphism. A compactBanach–Alaoglu theorem (8,306 words) [view diff] exact match in snippet view article find links to article
( X ∖ U ) {\displaystyle X=U\,\cup \,(X\setminus U)} then the linear bijection H : ∏ x ∈ X K → ( ∏ u ∈ U K ) × ∏ x ∈ X ∖ U K ( f x ) x ∈ X ↦ ( ( f uVon Neumann paradox (1,526 words) [view diff] exact match in snippet view article find links to article
big figure to a subset of the A points in it, we can make a mapping (a bijection) from the big figure to all the A points in it. (In some regions pointsSuper vector space (1,893 words) [view diff] exact match in snippet view article find links to article
H o m ( V , − ) {\displaystyle \mathrm {Hom} (V,-)} , given a natural bijection H o m ( U ⊗ V , W ) ≅ H o m ( U , H o m ( V , W ) ) . {\displaystyle \mathrmTelephone number (mathematics) (2,039 words) [view diff] exact match in snippet view article
(7): 1004–1013, doi:10.1089/cmb.2005.12.1004, PMID 16201918 A direct bijection between involutions and tableaux, inspired by the recurrence relationKleinian group (2,344 words) [view diff] exact match in snippet view article find links to article
invariant component D A conjugate of an element h of H by a conformal bijection is parabolic or elliptic if and only if h is. Any parabolic element ofSuper vector space (1,893 words) [view diff] exact match in snippet view article find links to article
H o m ( V , − ) {\displaystyle \mathrm {Hom} (V,-)} , given a natural bijection H o m ( U ⊗ V , W ) ≅ H o m ( U , H o m ( V , W ) ) . {\displaystyle \mathrmDrinfeld module (1,623 words) [view diff] exact match in snippet view article find links to article
conjectures for function fields state (very roughly) that there is a bijection between cuspidal automorphic representations of GLn and certain representationsCommutative ring (5,688 words) [view diff] exact match in snippet view article find links to article
algebraically closed field k, mSpec (k[T1, ..., Tn] / (f1, ..., fm)) is in bijection with the set {x =(x1, ..., xn) ∊ kn Thus, maximal ideals reflect the geometricKostka number (1,255 words) [view diff] exact match in snippet view article find links to article
immediately obvious from the definition but can be shown by establishing a bijection between the sets of semistandard Young tableaux of shape λ {\displaystyleEisenstein series (3,533 words) [view diff] exact match in snippet view article find links to article
{\displaystyle (m,n)\mapsto (m,n){\begin{pmatrix}d&c\\b&a\end{pmatrix}}} is a bijection Z {\displaystyle \mathbb {Z} } 2 → Z {\displaystyle \mathbb {Z} } 2, iHidden Field Equations (2,622 words) [view diff] exact match in snippet view article find links to article
{\displaystyle P(x')=y'} . Since P {\displaystyle P} is not necessary a bijection, one may find more than one solution to this inversion (there exist atBeauville–Laszlo theorem (1,161 words) [view diff] exact match in snippet view article find links to article
trivialization over DR. Then the maps in the above diagram furnish a bijection between Triv(XR) and GLr(R((t))) (where R((t)) is the formal Laurent seriesExtensive-form game (3,759 words) [view diff] exact match in snippet view article find links to article
a_{v}:s(v)\rightarrow A(H)} of a {\displaystyle a} on s ( v ) {\displaystyle s(v)} is a bijection, with s ( v ) {\displaystyle s(v)} the set of successor nodes of v {\displaystyleSpringer correspondence (847 words) [view diff] exact match in snippet view article find links to article
by the partitions of n. The Springer correspondence in this case is a bijection, and in the standard parametrizations, it is given by transposition ofBornological space (3,804 words) [view diff] exact match in snippet view article find links to article
{B}})\subseteq {\mathcal {C}}.} If in addition f {\displaystyle f} is a bijection and f − 1 {\displaystyle f^{-1}} is also bounded then f {\displaystyleGoursat's lemma (1,513 words) [view diff] exact match in snippet view article find links to article
G / N ≅ G ′ / N ′ {\displaystyle G/N\cong G'/N'} . One then obtains a bijection between: Subgroups of G × G ′ {\displaystyle G\times G'} which projectString diagram (3,699 words) [view diff] exact match in snippet view article find links to article
convenient to encode string diagrams as formulae in generic form, which are in bijection with the labeled generic progressive plane graphs defined above. Fix aComplemented subspace (3,308 words) [view diff] exact match in snippet view article find links to article
identity map X → Y {\displaystyle X\to Y} is then a continuous, linear bijection but its inverse is not continuous, since X {\displaystyle X} has a finerPigeonhole principle (4,184 words) [view diff] exact match in snippet view article find links to article
injective, then there exists an element b of B such that there exists a bijection between the preimage of b and A. This is a quite different statement,Vector bornology (1,471 words) [view diff] exact match in snippet view article find links to article
{B}}\right)\subseteq {\mathcal {C}}.} If in addition f {\displaystyle f} is a bijection and f − 1 {\displaystyle f^{-1}} is also bounded then f {\displaystyleSchröder–Bernstein property (1,039 words) [view diff] exact match in snippet view article find links to article
left/mid); yet, both aren't similar. The Schröder-Bernstein theorem applied to the unstructured pixel sets obtains a non-continuous bijection (right).Inner product space (7,357 words) [view diff] exact match in snippet view article find links to article
{\displaystyle L} and let φ : F → B {\displaystyle \varphi :F\to B} be a bijection. Then there is a linear transformation T : K → L {\displaystyle T:K\toModuli stack of principal bundles (896 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \pi _{0}(\operatorname {Bun} _{G}(X))} is in a natural bijection with the fundamental group π 1 ( G ) {\displaystyle \pi _{1}(G)} . ThisLinear system of divisors (2,910 words) [view diff] exact match in snippet view article find links to article
nonsingular projective variety, the set | D | {\displaystyle |D|} is in natural bijection with ( Γ ( X , L ) ∖ { 0 } ) / k ∗ , {\displaystyle (\Gamma (X,{\mathcalBaxter permutation (973 words) [view diff] exact match in snippet view article find links to article
Technology. Ackerman, Eyal; Barequet, Gill; Pinter, Ron Y. (2006), "A bijection between permutations and floorplans, and its applications", Discrete AppliedLinear system of divisors (2,910 words) [view diff] exact match in snippet view article find links to article
nonsingular projective variety, the set | D | {\displaystyle |D|} is in natural bijection with ( Γ ( X , L ) ∖ { 0 } ) / k ∗ , {\displaystyle (\Gamma (X,{\mathcalOrder polynomial (1,272 words) [view diff] exact match in snippet view article find links to article
generalize the linear extensions of P {\displaystyle P} , the order-preserving bijections ϕ : P ⟶ ∼ [ p ] {\displaystyle \phi :P{\stackrel {\sim }{\longrightarrowJ-invariant (4,738 words) [view diff] exact match in snippet view article find links to article
elliptic curve iff τ = T(τ') for some T ∈ PSL(2, Z). This means j provides a bijection from the set of elliptic curves over C to the complex plane. As a RiemannFreiling's axiom of symmetry (1,818 words) [view diff] exact match in snippet view article find links to article
= κ + {\displaystyle 2^{\kappa }=\kappa ^{+}\,} . Then there exists a bijection σ : κ + → P ( κ ) {\displaystyle \sigma :\kappa ^{+}\to {\mathcal {P}}(\kappaVeblen function (2,749 words) [view diff] exact match in snippet view article find links to article
smaller limit ordinals, then one can create an explicit constructive bijection between ω and α, (i.e. one not using the axiom of choice). Here we willStiefel manifold (2,141 words) [view diff] exact match in snippet view article find links to article
an n-dimensional vector space X, the dual basis construction gives a bijection between bases for X and bases for the dual space X ∗ , {\displaystyleBasis of a matroid (1,639 words) [view diff] exact match in snippet view article find links to article
basis-exchange property. Bijective basis-exchange property: There is a bijection f {\displaystyle f} from A {\displaystyle A} to B {\displaystyle B} ,Default logic (3,222 words) [view diff] exact match in snippet view article find links to article
logic; a translation is faithful if there exists a mapping (typically, a bijection) between the extensions (or models) of the original and translated theories;Logarithm (11,674 words) [view diff] exact match in snippet view article find links to article
has range R > 0 {\displaystyle \mathbb {R} _{>0}} . Therefore, f is a bijection from R {\displaystyle \mathbb {R} } to R > 0 {\displaystyle \mathbb {R}Pregeometry (model theory) (2,037 words) [view diff] exact match in snippet view article
automorphism of a pregeometry ( S , cl ) {\displaystyle (S,{\text{cl}})} is a bijection σ : S → S {\displaystyle \sigma :S\to S} such that σ ( cl ( X ) ) = clOrbit portrait (2,084 words) [view diff] exact match in snippet view article find links to article
{\mathbb {R} }/{\mathbb {Z} }} The doubling map on the circle gives a bijection from A j {\displaystyle A_{j}} to A j + 1 {\displaystyle A_{j+1}} andTime dependent vector field (1,013 words) [view diff] exact match in snippet view article find links to article
x t ↔ ( t , x t ) {\displaystyle x_{t}\leftrightarrow (t,x_{t})} is a bijection between the sets of integral curves of X {\displaystyle X} and X ~ , {\displaystyleGenus of a multiplicative sequence (2,718 words) [view diff] exact match in snippet view article find links to article
generators of degree 4k for positive integers k, implies that this gives a bijection between formal power series Q with rational coefficients and leading coefficientLehmer code (2,105 words) [view diff] exact match in snippet view article find links to article
reconstructing the sequence B,F,A,G,D,E,C. The Lehmer code defines a bijection from the symmetric group Sn to the Cartesian product [ n ] × [ n − 1 ]Semigroup action (1,971 words) [view diff] exact match in snippet view article find links to article
Currying). Because curry {\displaystyle \operatorname {curry} } is a bijection, semigroup actions can be defined as functions S → ( X → X ) {\displaystyleConstant-mean-curvature surface (2,037 words) [view diff] exact match in snippet view article find links to article
the plane which are of finite type. More precisely there is an explicit bijection between CMC immersions of R 2 {\displaystyle \mathbb {R} ^{2}} into RProjective plane (6,933 words) [view diff] exact match in snippet view article find links to article
points and lines to lines that preserves incidence, meaning that if σ is a bijection and point P is on line m, then Pσ is on mσ. If σ is a collineation ofPauli matrices (7,495 words) [view diff] exact match in snippet view article find links to article
{\vec {a}}\cdot {\vec {\sigma }}} , making it manifest that the map is a bijection. The norm is given by the determinant (up to a minus sign) det ( a → ⋅Differential entropy (2,842 words) [view diff] exact match in snippet view article find links to article
{\displaystyle m} . The above inequality becomes an equality if the transform is a bijection. Furthermore, when m {\displaystyle m} is a rigid rotation, translationExotic sphere (3,875 words) [view diff] exact match in snippet view article find links to article
be assigned to exactly one point in the unit n-sphere by a continuous bijection with continuous inverse. For example, a point x on an n-sphere of radiusInformation theory and measure theory (1,762 words) [view diff] exact match in snippet view article find links to article
such that either one is completely determined by the other (i.e. by a bijection); where μ {\displaystyle \mu } is a signed measure over these sets, andBalanced category (201 words) [view diff] exact match in snippet view article find links to article
The category of topological spaces is not balanced (since continuous bijections are not necessarily homeomorphisms), while a topos is balanced. This isSmooth projective plane (1,679 words) [view diff] exact match in snippet view article find links to article
manifold. Automorphisms play a crucial role in the study of smooth planes. A bijection of the point set of a projective plane is called a collineation, if itExtensions of symmetric operators (3,248 words) [view diff] exact match in snippet view article find links to article
only if the deficiency indices are both zero. We see that there is a bijection between symmetric extensions of an operator and isometric extensions ofPolynomial ring (8,646 words) [view diff] exact match in snippet view article find links to article
polynomial ring means that F and POL are adjoint functors. That is, there is a bijection Hom S E T ( X , F ( A ) ) ≅ Hom A L G ( K [ X ] , A ) . {\displaystyle