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 ?
They introduce and analyze the underlying topological structures, then work out the connection to the spin condition in differential topology.
A large number of theories regarding uncertainty with their respective topological structures have been introduced.
In fact, as already demonstrated in optics, the superposition of vortex beams can generate a wide variety of topological structures of phase and intensity, such as loops, links and knots in 3D space [27], or interesting polarization topologies [28, 29].
This new approach should be applicable in any quantum system - whether the qubits rely on superconductors, trapped ions, semiconductors, or topological structures (should they need them).
These two coupled single-layer networks, whose topological structures may be different, can be viewed as a two-layer network.
The Topological Structures of [K.sup.M.sub.l](R) and [K.sup.M.sub.l](C)
Meanwhile the drug targets have special topological structures that are different with normal proteins.
These partial results show that, the answer to this question is very related to the geometrical and topological structures of K.
In addition to confirming the existence of 83 previously reported areas and identifying 97 new ones, the map also reveals topological structures that vary from person to person.
However, among these references, only the work in [23] considers projective synchronization between two FCNs with identical nodes and identical topological structures. Thus, it is necessary to construct a more general projective synchronization scheme between two coupled FCNs.
Motivated by the above discussions, generalized outer synchronization between two dynamical networks with unknown parameters is investigated, where nodes in the two networks may have identical or different dynamics and the topological structures are different.

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