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searching for Family of sets 74 found (155 total)

alternate case: family of sets

Intersection graph (1,137 words) [view diff] exact match in snippet view article find links to article

graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph, but some important

In mathematics, specifically set theory, a cumulative hierarchy is a family of sets Wα{\displaystyle W_{\alpha }} indexed by ordinals α{\displaystyle \alpha

being a property of a specific set, identity is, by extension, the "family" of sets or set forms which satisfy a possible identity. These families are

In combinatorics, a Helly family of order k is a family of sets in which every minimal subfamily with an empty intersection has k or fewer sets in it.

item that is not in R is not close to 0. In general, one refers to the family of sets containing 0, used to approximate 0, as a neighborhood basis; a member

spin quantum number equal to 1 Vector measure, a function defined on a family of sets and taking vector values satisfying certain properties Vector meson

with uncertainty in a parametric manner. A soft set is a parameterised family of sets - intuitively, this is "soft" because the boundary of the set depends

of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There are flourishing

A\cap E} has the Baire property relative to E {\displaystyle E} . The family of sets with the property of Baire forms a σ-algebra. That is, the complement

a special subset of a partially ordered set Filter (set theory) – Family of sets representing "large" sets Ideal (order theory) – Nonempty, upper-bounded

In mathematical set theory, a pseudo-intersection of a family of sets is an infinite set S such that each element of the family contains all but a finite

unique estimate of the parameter, we are interested in constructing a family of sets that contain the true (unknown) parameter value with a specified probability

sets are Lebesgue-measurable. (Not a consequence of 2 and 3, because a family of sets that is closed under complements and disjoint countable unions does

A zero-suppressed decision diagram (ZSDD or ZDD) is a particular kind of binary decision diagram (BDD) with fixed variable ordering. This data structure

If { A i } i ∈ I {\displaystyle \left\{A_{i}\right\}_{i\in I}} is a family of sets indexed by another set, one can form the disjoint union or coproduct

{\displaystyle x} . In other words, an ultrafilter may be seen as a family of sets which "locally" resembles a principal ultrafilter.[citation needed]

\bigcup _{i}E_{i})=\sum _{i}P(X\in E_{i})} for any countable disjoint family of sets { E i } {\displaystyle \{E_{i}\}} The concept of probability function

set of all the fibers over the elements of Y {\displaystyle Y} is a family of sets indexed by Y . {\displaystyle Y.} For example, for the function f (

would belong to U, as every set has the empty set as a subset. Any family of sets that satisfies (2–4) is called a filter (an example: the complements

zero satisfying the Lebesgue's regularity condition, defined above as family of sets with bounded eccentricity. This follows since the same substitution

exist an edge (x,z). One can represent any finite partial order as a family of sets, such that x < y in the partial order whenever the set corresponding

(in the category theoretic sense) is the Cartesian product. Given a family of sets X i {\displaystyle X_{i}} the product is defined as ∏ i ∈ I X i := {

\bigsqcup {\text{ or }}\coprod } 1.  Used for the disjoint union of a family of sets, such as in ⨆ i ∈ I A i . {\textstyle \bigsqcup _{i\in I}A_{i}.} 2.  Denotes

description of the graph, the conjecture may be restated as follows: if some family of sets has n total elements, and any two sets intersect in at most one element

variables. An antichain of sets (also known as a Sperner family) is a family of sets, none of which is contained in any other set. If V is a set of n Boolean

the cliques of G. Any subset of a clique is itself a clique, so this family of sets meets the requirement of an abstract simplicial complex that every subset

mathematical ring that absorbs multiplication Ideal (set theory) – Non-empty family of sets that is closed under finite unions and subsets Semigroup ideal Boolean

Loosely speaking, dependent types are similar to the type of an indexed family of sets. More formally, given a type A : U {\displaystyle A:{\mathcal {U}}}

prize offered by Chvátal for its solution) he suggested that, in any family of sets closed under the operation of taking subsets, the largest pairwise-intersecting

tree. The diamond principle ◊ says that there exists a ◊-sequence, a family of sets Aα ⊆ α for α < ω1 such that for any subset A of ω1 the set of α with

Collection of open sets used to define a topology Filter (set theory) – Family of sets representing "large" sets Filters in topology – Use of filters to describe

an indexed family of functions fn, whereas the latter is an indexed family of sets of functions E n {\displaystyle {\mathcal {E}}^{n}} . (See Points of

compute this covering graph efficiently; more generally, if B is any family of sets, they show how to compute the covering graph of the lattice of unions

partition function of statistical mechanics. Filter (set theory) – Family of sets representing "large" sets Filters in topology – Use of filters to describe

a, fails to be a cover of S. Indeed, the intersection of the finite family of sets VU is a neighborhood W of a in Rn. Since a is a limit point of S, W

context: Ω {\displaystyle \Omega } is the disjoint union of a countable family of sets in S . {\displaystyle {\mathcal {S}}.} A field of sets (respectively

< ε and where the convergence is also uniform. Consider the indexed family of sets whose index set is the set of natural numbers m ∈ N , {\displaystyle

well-ordering theorem, Zorn's lemma, and the Hausdorff maximal principle. A family of sets F {\displaystyle {\mathcal {F}}} is of finite character provided it

matroid when it is linearly independent in the vector space. Every family of sets constructed in this way is a matroid, but not every matroid can be constructed

complement of an open set is closed, and vice versa. In matroid theory, the family of sets complementary to the independent sets of a given matroid themselves

edges Testing whether the Vapnik–Chervonenkis dimension of a given family of sets is below a given bound Ladner, Richard (1975). "On the Structure of

cliques of a graph). Every graph is an intersection graph for some family of sets, and this family is called an intersection representation of the graph

uniform spaces in terms of a family of pseudometrics. Coarse structure – family of sets in geometry and topology to measure large-scale properties of a spacePages

metrizable if and only if it is regular and T0 and has a σ-discrete basis. A family of sets is called σ-discrete when it is a union of countably many discrete collections

neighborhood base of the origin in X . {\displaystyle X.} Then the family of sets { cl C ⁡ N : N ∈ N } {\displaystyle \left\{\operatorname {cl} _{C}N:N\in

a special subset of a partially ordered set Filter (set theory) – Family of sets representing "large" sets Filters in topology – Use of filters to describe

{\displaystyle r>2} ? Frankl's union-closed sets conjecture – for any family of sets closed under sums there exists an element (of the underlying space)

triangle. Set TSP problem, a more general task of visiting each of a family of sets by the shortest tour Heinrich Dörrie: 100 Great Problems of Elementary

subnet that converges to x . {\displaystyle x.} Filter (set theory) – Family of sets representing "large" sets Filters in topology#Subnets – Use of filters

algorithms, a weak ordering on the vertices of a graph (represented as a family of sets that partition the vertices, together with a doubly linked list providing

A} to produce | F ∗ | {\displaystyle |F^{*}|} many sets. Denote this family of sets F A {\displaystyle F_{A}} . Take the union of F A {\displaystyle F_{A}}

{\displaystyle G} is an undirected graph, and F {\displaystyle F} is the family of sets of edges that form forests in G {\displaystyle G} , then F {\displaystyle

Characterizations of the category of topological spaces Filter (set theory) – Family of sets representing "large" sets Filters in topology – Use of filters to describe

considered by Lovász in 1975. In this problem, one is given as input a family of sets F = {S0, S1, ...}; the task is to find a subfamily, with as few sets

triangle containing two or more degree-two vertices. A clique complex is a family of sets of vertices of a graph G {\displaystyle G} that induce complete subgraphs

{\displaystyle I} be a set of indices and C {\displaystyle C} be a family of sets ( U i ) i ∈ I {\displaystyle (U_{i})_{i\in I}} . The nerve of C {\displaystyle

50s[clarification needed], much work has gone into formalizing this complexity. The family of sets of uniqueness, considered as a set inside the space of compact sets

the empty set. This is because the empty set is covered by the empty family of sets: Vacuously, any two sections of F {\displaystyle F} over the empty set

strictest family of sets whose elements are consistent with the prior information. Since there is, usually, no known worst case, the family of sets may be

for which the preimage of a measurable set is measurable π-system – Family of sets closed under intersection Ring of sets – Family closed under unions

symmetric difference operator preserves the property of being Eulerian. A family of sets closed under the symmetric difference operation can be described algebraically

Obviously those balls are pairwise disjoint, and also are an indexed family of sets whose index set is [ 0 , 1 ] {\displaystyle [0,1]} . This implies that

in this way is O(|X|), independent of the number of elements in the family of sets and also independent of the total number of sets in the data structure

dimension 5 or more.: 9–11  An abstract simplicial complex (ASC) is family of sets that is closed under taking subsets (the subset of a set in the family

surfaces as oriented boundaries of sets in space. Also in this paper, the family of sets approximable by polygonal domains of finite perimeter, known today as

for metric spaces: Every basis of the topology contains a countable family of sets with vanishing diameters that covers the space. Soon thereafter, Witold

matroid gives the cardinality of a minimum even set, a subcollection of a family of sets that includes an even number of copies of each set element. Determining

\scriptstyle M} , Q i {\displaystyle \scriptstyle Q_{i}} denotes the family of sets whose independence differs from M {\displaystyle \scriptstyle M} to

\tau \circ \alpha =\alpha _{\sigma }^{\tau }\circ \sigma .} Then the family of sets N={NX; X∈Ob⁡(K)}{\displaystyle {\mathcal {N}}=\{{\mathcal {N}}^{X};\

as its integral, or replace the single set S{\displaystyle S} with a family of sets. A computational problem related to Blichfeldt's theorem has been shown

{\displaystyle \mu (\cup _{n\geq 1}\{x=T^{n}x\})=0} A Rokhlin tower is a family of sets S , T S , … , T N − 1 S {\textstyle S,TS,\dots ,T^{N-1}S} that are disjoint

in ): Hunter formulated a conjecture (1991) bounding the size of a family of sets under intersection constraints. He conjectured that if L {\displaystyle

a special subset of a partially ordered set Filter (set theory) – Family of sets representing "large" sets Generalized quantifier – Expression denoting

n d o , e x o ) {\displaystyle SM_{n}(gevol,endo,exo)} denotes the family of sets of vectors of natural numbers computed by using at most $n$ membranes