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Longer titles found: Finite topological space (view), Noetherian topological space (view), Localization of a topological space (view), Axiomatic foundations of topological spaces (view), Quasitopological space (view), Category of topological spaces (view), Complete topological space (view), N-topological space (view), Pretopological space (view)

searching for Topological space 59 found (1153 total)

alternate case: topological space

∞-topos (287 words) [view diff] exact match in snippet view article find links to article

example of an ∞-topos is the ∞-category of sheaves of spaces on some topological space. But the notion is more flexible; for example, the ∞-category of étale

Bounded set (733 words) [view diff] exact match in snippet view article find links to article

called unbounded. The word "bounded" makes no sense in a general topological space without a corresponding metric. Boundary is a distinct concept: for

Luzin space (536 words) [view diff] no match in snippet view article find links to article

In mathematics, a Luzin space (or Lusin space), named for N. N. Luzin, is an uncountable topological T1 space without isolated points in which every nowhere-dense

Sion's minimax theorem (210 words) [view diff] exact match in snippet view article find links to article

compact convex subset of a linear topological space and Y{\displaystyle Y} a convex subset of a linear topological space. If f{\displaystyle f} is a real-valued

Natural topology (366 words) [view diff] exact match in snippet view article find links to article

subspaces and quotient spaces. The natural topology on a subset of a topological space is the subspace topology. This is the coarsest topology which makes

Functor category (1,742 words) [view diff] exact match in snippet view article find links to article

The category of presheaves on a topological space X{\displaystyle X} is a functor category: we turn the topological space into a category C{\displaystyle

Lie algebra bundle (540 words) [view diff] exact match in snippet view article find links to article

Hausdorff. But if all fibres of a real Lie algebra bundle over a topological space are mutually isomorphic as Lie algebras, then it is a locally trivial

3-torus (234 words) [view diff] exact match in snippet view article find links to article

The three-dimensional torus, or 3-torus, is defined as any topological space that is homeomorphic to the Cartesian product of three circles, T3=S1×S1×S1

Dispersion point (242 words) [view diff] exact match in snippet view article find links to article

point in a topological space the removal of which leaves the space highly disconnected. More specifically, if X is a connected topological space containing

Identity component (868 words) [view diff] exact match in snippet view article find links to article

group G over a field k is the identity component of the underlying topological space. The identity component of a group scheme G over a base scheme S is

Homology manifold (252 words) [view diff] exact match in snippet view article find links to article

homology manifold (or generalized manifold) is a locally compact topological space X that looks locally like a topological manifold from the point of

Homotopical connectivity (3,209 words) [view diff] exact match in snippet view article find links to article

algebraic topology, homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical connectivity

Compact quantum group (1,526 words) [view diff] exact match in snippet view article find links to article

continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C*-algebra up to homeomorphism

Phragmen–Brouwer theorem (242 words) [view diff] exact match in snippet view article find links to article

Brouwer, states that if X is a normal connected locally connected topological space, then the following two properties are equivalent: If A and B are

Fibered manifold (1,445 words) [view diff] exact match in snippet view article find links to article

that for Seifert what is now called the base space (topological space) of a fiber (topological) space E{\displaystyle E} was not part of the structure,

Excision theorem (651 words) [view diff] exact match in snippet view article find links to article

relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space X{\displaystyle X} and subspaces A{\displaystyle A} and U{\displaystyle

Tensor product bundle (284 words) [view diff] exact match in snippet view article find links to article

Thus, the set of the isomorphism classes of all line bundles on some topological space X forms an abelian group called the Picard group of X. One can also

Poincaré complex (616 words) [view diff] exact match in snippet view article find links to article

the abstract properties of Poincaré duality. A Poincaré space is a topological space whose singular chain complex is a Poincaré complex. These are used

Moduli stack of principal bundles (800 words) [view diff] exact match in snippet view article find links to article

Replacing the quotient stack (which is not a topological space) by a homotopy quotient (which is a topological space) gives the homotopy type of BunG⁡(X){\displaystyle

Glossary of algebraic topology (7,302 words) [view diff] exact match in snippet view article find links to article

Xn=ΣnX{\displaystyle X_{n}=\Sigma ^{n}X}. stratified 1. A stratified space is a topological space with a stratification. 2. A stratified Morse theory is a Morse theory

Handle decomposition (1,755 words) [view diff] exact match in snippet view article find links to article

handle decomposition is to a manifold what a CW-decomposition is to a topological space—in many regards the purpose of a handle decomposition is to have a

Dense order (738 words) [view diff] exact match in snippet view article find links to article

a subset of a topological space whose closure is the whole space Dense-in-itself — a subset A{\displaystyle A} of a topological space such that A{\displaystyle

List of mathematical properties of points (400 words) [view diff] exact match in snippet view article find links to article

of a topological space, such that every open neighbourhood of p contains uncountably many points of S Limit point, a set S in a topological space X is

Closed graph theorem (functional analysis) (4,695 words) [view diff] exact match in snippet view article

{\displaystyle y\in Y,} then y=0.{\displaystyle y=0.} Every metrizable topological space is pseudometrizable. A pseudometrizable space is metrizable if and

Topological half-exact functor (172 words) [view diff] exact match in snippet view article find links to article

examples of contravariant half-exact functors. If B is any fibrant topological space, the (representable) functor F(X)=[X,B] is half-exact. https://math

Homological connectivity (874 words) [view diff] exact match in snippet view article find links to article

algebraic topology, homological connectivity is a property describing a topological space based on its homology groups. X is homologically-connected if its

Nikolai Shanin (99 words) [view diff] exact match in snippet view article find links to article

mathematics. He introduced the delta-system lemma and the caliber of a topological space. Vsemirnov, M A, "Nikolai Aleksandrovich Shanin (on his 80th birthday)"

Nerve complex (1,577 words) [view diff] exact match in snippet view article find links to article

(Ui)i∈I{\displaystyle (U_{i})_{i\in I}} are open subsets of some topological space X{\displaystyle X}. The set N(C){\displaystyle N(C)} may contain singletons

Boundary tracing (1,057 words) [view diff] exact match in snippet view article find links to article

Boundary is a topological notion. However, a digital image is no topological space. Therefore, it is impossible to define the notion of a boundary in

Uniform absolute-convergence (438 words) [view diff] exact match in snippet view article find links to article

on all compact subsets of a topological space, it is compactly (uniformly) absolutely-convergent. If the topological space is locally compact, these notions

Irreducible ring (564 words) [view diff] exact match in snippet view article find links to article

irreducible spectrum is a ring whose spectrum is irreducible as a topological space. "Meet-irreducible" rings are referred to as "irreducible rings" in

Quillen spectral sequence (182 words) [view diff] exact match in snippet view article find links to article

spectral sequence converging to the sheaf cohomology of a type of topological space that occurs in algebraic geometry. It is used in calculating the homotopy

Proj construction (3,567 words) [view diff] no match in snippet view article find links to article

In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical

Michael selection theorem (870 words) [view diff] exact match in snippet view article find links to article

X\to Y} of F. Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values, admits a

Sigma-ideal (550 words) [view diff] exact match in snippet view article find links to article

power set of the underlying set. For example, the meager subsets of a topological space are those in the 𝜎-ideal generated by the collection of closed subsets

Torus (4,970 words) [view diff] exact match in snippet view article find links to article

torus, a surface in 4-space. In the field of topology, a torus is any topological space that is homeomorphic to a torus. The surface of a coffee cup and a

Discrete (172 words) [view diff] exact match in snippet view article find links to article

variable that can be counted Discrete space, a simple example of a topological space Discrete spline interpolation, the discrete analog of ordinary spline

Topological entropy (1,656 words) [view diff] exact match in snippet view article find links to article

measure-theoretic entropy. A topological dynamical system consists of a Hausdorff topological space X (usually assumed to be compact) and a continuous self-map f : X → X

Fiber functor (757 words) [view diff] exact match in snippet view article find links to article

Set{\displaystyle {\mathfrak {Set}}}. If we have the topos of sheaves on a topological space X{\displaystyle X}, denoted T(X){\displaystyle {\mathfrak {T}}(X)}

Cosheaf (361 words) [view diff] exact match in snippet view article find links to article

admits colimits is a functor F from the category of open subsets of a topological space X (more precisely its nerve) to C such that (1) The F of the empty

Component (274 words) [view diff] exact match in snippet view article find links to article

Connected component (topology), a maximal connected subspace of a topological space Vector component, result of the decomposition of a vector into various

Germ (256 words) [view diff] exact match in snippet view article find links to article

diseases are caused by microorganisms Germ (mathematics), an object in a topological space that captures local properties Germs (band), an American punk rock

Compact group (4,392 words) [view diff] exact match in snippet view article find links to article

group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within

Named set theory (1,919 words) [view diff] exact match in snippet view article find links to article

set are names) and fiber bundles (objects form a topological space, names from another topological space and the connection is a continuous projection)

Dispersion (422 words) [view diff] exact match in snippet view article find links to article

dispersion of a probability distribution Dispersion point, a point in a topological space the removal of which leaves the space highly disconnected The dependence

Origin (mathematics) (386 words) [view diff] exact match in snippet view article

a vector space Distance from a point to a plane Pointed space, a topological space with a distinguished point Radial basis function, a function depending

Partition (316 words) [view diff] exact match in snippet view article find links to article

Partition of a set, grouping elements of a set Partition of unity, of a topological space Plane partition, in mathematics and especially combinatorics Graph

Graph homology (2,186 words) [view diff] exact match in snippet view article find links to article

the homology groups of a graph, where the graph is considered as a topological space. It formalizes the idea of the number of "holes" in the graph. It

Relative homology (2,455 words) [view diff] exact match in snippet view article find links to article

algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for

Profinite word (1,012 words) [view diff] exact match in snippet view article find links to article

are a generalization of the notion of finite words into a complete topological space. This notion allows the use of topology to study languages and finite

Unit square (264 words) [view diff] exact match in snippet view article find links to article

square can also be thought of as a subset of the complex plane, the topological space formed by the complex numbers. In this view, the four corners of the

Locally compact group (1,005 words) [view diff] exact match in snippet view article find links to article

a fallback Locally compact field Locally compact space – Type of topological space in mathematics Locally compact quantum group – relatively new C*-algebraic

Regular (961 words) [view diff] exact match in snippet view article find links to article

power of the matrix are positive Free regular set, a subset of a topological space that is acted upon disjointly under a given group action Regular homotopy

Base (578 words) [view diff] exact match in snippet view article find links to article

nontrivial group element. Base (topology), a type of generating set for a topological space Backward Society Education, a Nepali non-governmental organization

Overcategory (737 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {C}}} is a categorical generalization of a topological space first introduced by Grothendieck. One of the canonical examples comes

0th (127 words) [view diff] exact match in snippet view article find links to article

refer to: 0th or zeroth, an ordinal for the number 0 0th dimension, a topological space 0th element, of a data structure in computer science 0th law of Thermodynamics

Corona (780 words) [view diff] exact match in snippet view article find links to article

kind of binary operation on two graphs Corona set (or corona), of a topological space Corona (fluid dynamics), the last phase of a drop's impact on a liquid

Charles Earl Rickart (284 words) [view diff] case mismatch in snippet view article find links to article

Henry Hildebrandt with the thesis Integration in a Convex Linear Topological Space. Rickart was for two years the Benjamin Pierce Instructor at Harvard

Subspace (222 words) [view diff] exact match in snippet view article find links to article

space inheriting all characteristics of a parent space A subset of a topological space endowed with the subspace topology Linear subspace, in linear algebra