topological space

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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:
Noun1.topological space - (mathematics) any set of points that satisfy a set of postulates of some kindtopological space - (mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional"
infinite, 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 arrangement
set - (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"
subspace - a space that is contained within another space
null space - a space that contains no points; and empty space
manifold - a set of points such as those of a closed surface or an analogue in three or more dimensions
metric 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 ?
The space exp(X) is endowed with the Vietoris topology. Recall that the Vietoris topology is generated by the open base of all collections of the form e(V) = {F [member of] exp(X): F [subset] UV, F [intersection] V [not equal to] [??] for any V [member of] V}, where V runs over the finite families of open subsets of X.
Among these are the Hausdorff metric topology (for a metric space) introduced in [6] and the Vietoris topology introduced in [12].
(a) A subbasis for the lower Vietoris topology, [tau]([V.sup.-]), consists of sets of the form [U.sup.-] for all open subsets U of X.