Topological Spaces

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

Chapter Chapter 2 in Encyclopedia of Distances, 2016, pp 63-70 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; Topological Vector Space; Polish Space (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-662-52844-0_2

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