topological space

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topological space

n.
A set of points together with a topology defined on them.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
topologický prostor
topologisk rum
topologinen avaruus
espace topologique
topološki prostor
spazio topologico
espaço topológico
References in periodicals archive ?
We have Throughout this paper neutrosophic topological spaces (briefly NTS) ([S.sub.1],[[xi].sub.1]),([S.sub.2], [[xi].sub.2]) and ([S.sub.3], [[xi].sub.3]) will be replaced by [S.sub.1],[S.sub.2] and [S.sub.3], respectively.
Later, topological structures in fuzzy topological spaces [5] were generalized to intuitionistic fuzzy topological spaces by Coker in [4], who then introduced the concept of an intuitionistic set [4].
The second half of the book examines weak convergences of measures on topological spaces, the sequences of measures, and the topological properties of spaces of measures on topological spaces connected with other properties of the spaces on which measures are defined.
Peleg, "Utility functions for partially ordered topological spaces," Econometrica, vol.
(3) If a bitopological space (X,[[tau].sub.1],[[tau].sub.2]) is [[tau].sub.1][[tau].sub.2]-[delta] semiconnected, then the topological spaces (X, [[tau].sub.1] ] and (X, [[tau].sub.2]) are 5-semiconnected.
In this paper, we firstly establish a new existence result of Nash equilibria for discontinuous games in general topological spaces with binary relations.
Our aim in this review is to collect the basic properties of our multimap classes and some mutual relations among them in general topological spaces or our abstract convex spaces.
Shabir introduced soft topological spaces and established that every soft topological space induce a parameterized family of topological spaces.
CW-Complexes and Their Quotient Spaces, Particular Point Topological Spaces, and Excluded Point Topological Spaces
The theory of soft topological spaces is investigated by defining a new soft set theory which can lead to the development of new mathematical models.

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