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 ?
Objective: This two-year project aims at exploiting both the intrinsic robustness and wide diversity of topological structures that naturally appear in soft condensed matter systems such as liquid crystals in order to fabricate advanced materials, possibly reconfigurable, towards emerging photonics applications such as high-dimensional data storage and topological shaping of light at small scale.
Thron, Topological structures, Holt, Rinehart and Winston, New York, 1966.
In Section 4, we obtain all strong topological structures on finite dimensional PN spaces and show that each finite dimensional PN space is strongly complete.
Some existing scientific papers analyses the characteristics of the topological structures of existing dual-purpose wheelchair mechanisms with dual-functions of sitting and lying (Meng-Hui Hsu, 2009).
Among the topics are the functoriality of Rieffel's generalized fixed-point algebras for proper actions, division algebras and supersymmetry, Riemann-Roch and index formulae in twisted K-theory, noncommutative Yang-Mills theory for quantum Heisenberg manifolds, distances between matrix algebras that converge to coadjoint orbits, and geometric and topological structures related to M-branes.
Among the topological relations that are not applicable are ring configuration (no concentric polygons can be found), neighborhood order (because islands are disjoint), and topological structures (again, because islands are disjoint).

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