# 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
espace topologique
topološki prostor
spazio topologico
espaço topológico
References in periodicals archive ?
Both axioms M and G are valid in any particular point topological space.
A multilayer spatial model is a model that represents a specific space using several layers, such as a topological space layer and a sensor space layer, which are then combined .
When S is semi-topological, let S : S x X [right arrow] X be a representation of S on a topological space X.
The pair (f, [??]) is called a soft topological space over f and the members of [??] are said to be soft open in f.
A topologized group is a triple (Eq.) such that (Eq.) is a group and (Eq.) is a topological space. If both the multiplication (Eq.) and the inversion (Eq.) appings of (Eq.) are continuous, then (Eq.) is called a topological group.
Throughout this paper (X,[tau]) and (X,[[tau].sub.[alpha]]) will always be topological spaces. For a subset A of topological space X, Int(A), Cl(A), [Cl.sub.[alpha]](A) and [Int.sub.[alpha]](A) denote the interior, closure, [alpha]-closure and [alpha]-interior of A respectively and [G.sub.[alpha]] is the [alpha]-open set for topology [[tau].sub.[alpha]] on X.
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).
The subject of ideals in topological space has been studied by Kuratowski  and Vaidyanathaswamy .
The pair (L, [tau]) is called a topological space. A subset B of [tau] is called a base of [tau], if for each A [member of] [tau] and each x [member of] A, there exists B [member of] B such that x [member of] B [subset or equal to] A.
Let (X, [mu]) be a generalized topological space. Then
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. His topics include polynomial subclasses of Allen's algebra, binary qualitative formalisms, fuzzy reasoning, a categorical approach of qualitative reasoning, and applications and software tools.
A topological space (X, [tau]) is said to be sg*-normal if for any pair of disjoint sg-closed subsets F1 and F2 of X, there exist disjoint open sets U and V such that F1 [subset] U and F2 [subset] V .

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