# topological space

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Related to Topological structure: topology

## 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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
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
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
topologický prostor
topologisk rum
espace topologique
topološki prostor
spazio topologico
espaço topológico
References in periodicals archive ?
By using a hybrid model of these two mathematical techniques with a topological structure, we have developed the concept of single-valued neutrosophic soft topological K-algebras to analyze the element of indeterminacy in K-algebras.
The basic idea is to envision the nodes that k-hop away from a query node as an adaptive local dynamical system, where each node only interacts with its local topological structure. Relying on a proposed local distance dynamics model, the distances among nodes change over time, where the nodes sharing the same community with the query node tend to gradually move together, while other nodes stay far away from each other.
This peculiar topological structure was first observed at optical frequencies [23] and, as in our investigation, results from the proper superposition of different fields with topological singularities.
The topological structure of BPNN which consisted of input layer, hidden layer, and output layer was shown in Figure 4.
In the past few years, many efforts have been made to investigate various problems of multiplex networks, such as topological structure, dynamic behavior [2], synchronizability [3, 4], spectral property [5], diffusion process [6], and synchronization [7-10].
The composition and physicochemical character, signal peptide, subcellular localization, rans-membrane topological structure and hydrohobicity or hydrophilicity were analyzed by ProtParam at http://web.expasy.org/protparam, SignalP at http://www.cbs.dtu.dk/services/SignalP, TMHMM at http://www.cbs.dtu.dk/services/TMHMM, Wolfpsort at http://wolfpsort.org and ProtScale at http://web.expasy.org/protscale.
By defining the generalized node quality for the heterogeneous CPS terminals, the mutual influence of nodes and the spatial distribution of topological structure can be mathematically described.
In practical circumstances, the topological structure of a complex network is barely known exactly due to the weak cognition to the network complexity.
Mutual relationships between investors, investment banks and financial analysts, investment funds and listed companies, and so forth form the network topological structure of financial securities market.
Due to the complexity of topological structure and functional relationship within electromechanical systems, one of the component's failures may lead to another component's failure, which is called fault propagation.
Kandemir, "Topological structure of fuzzy soft sets," Computers & Mathematics with Applications, vol.

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