# topological space

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Related to topological space: metric space

## topological space

n.
A set of points together with a topology defined on them.

## topological space

n
(Mathematics) maths a set S with an associated family of subsets τ that is closed under set union and finite intersection. S and the empty set are members of τ
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 topological space - (mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"mathematical spaceinfinite, space - the unlimited expanse in which everything is located; "they tested his ability to locate objects in space"; "the boundless regions of the infinite"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementset - (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"subspace - a space that is contained within another spacenull space - a space that contains no points; and empty spacemanifold - a set of points such as those of a closed surface or an analogue in three or more dimensionsmetric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
Translations
topologický prostor
topologisk rum
topologinen avaruus
espace topologique
topološki prostor
spazio topologico
espaço topológico
References in periodicals archive ?
On the other hand, Coker  introduced the notions of an intuitionistic fuzzy topological space and some other related concepts.
Shabir introduced soft topological spaces and established that every soft topological space induce a parameterized family of topological spaces.
When S is semi-topological, let S : S x X [right arrow] X be a representation of S on a topological space X.
Let E be a Hausdorff topological space and U an open subset of E.
A subset of a topological space is said to be semi open, if there exists an open set in such that (Eq.
In the words of Belcher and his colleagues, we have been offered, theoretically as well as empirically, the chance to consider the camp as a topological space, that is to say, as a spatiality that is "always potential--that is, both capable of becoming and not becoming" (2008, page 502).
Two continuous functions from one topological space to another are called homotopic.
The subject of ideals in topological space has been studied by Kuratowski  and Vaidyanathaswamy .
Let (X, [lambda]) be a quasi topological space and A [subset or equal to] X.
A set A in a topological space (X,T) is semi-open, denoted by A[member of] SO(X,T), iff there exists an open set O such that O[subset or equal to] A[subset or equal to] Cl(O).
These entities could be considered points of a directed axis, he says--in temporal cases they could be time points, time intervals, or more complex entities; and in spatial cases could be points of the plane, regions of the plane, pairs of points, or even subspaces of a topological space.

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