Separability of Metric Spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1970Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 149, page 19 (issn: 0002-9947,

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Authors: Roy, P.;

doi: 10.2307/1995657 , 10.1090/s0002-9947-1970-0263020-1

Separability of Metric Spaces

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Abstract

A topological space S is separable means that some countable subset of S is dense in S. A subset T of a topological space is separable means that T has a countable subset which is dense in T. In view of the importance of this property, it is natural to inquire about conditions under which a space is separable. In this paper we shall discuss such conditions for metric spaces only(1). The following theorems give a few of the known conditions for separability

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