Topological Spaces

Michel Marie Deza and Elena Deza
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Michel Marie Deza: École Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 2 in Encyclopedia of Distances, 2013, pp 59-66 from Springer

Abstract: Abstract A topological space (X,τ) is a set X with a topology τ, i.e., a collection of subsets of X with the following properties: 1. X∈τ, ∅∈τ; 2. If A,B∈τ, then A∩B∈τ; 3. For any collection {A α } α , if all A α ∈τ, then ⋃ α A α ∈τ.

Keywords: Topological Space; Compact Space; Open Cover; Convex Space; Metrizable Space (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-30958-8_2

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DOI: 10.1007/978-3-642-30958-8_2

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