Uncountable Discrete Sets in Extensions and Metrizability
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Published:1982-12-01
Issue:4
Volume:25
Page:472-477
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Author:
Bell Murray,Ginsburg John
Abstract
AbstractIf X is a topological space then exp X denotes the space of non-empty closed subsets of X with the Vietoris topology and λX denotes the superextension of X Using Martin's axiom together with the negation of the continuum hypothesis the following is proved: If every discrete subset of exp X is countable the X is compact and metrizable. As a corollary, if λX contains no uncountable discrete subsets then X is compact and metrizable. A similar argument establishes the metrizability of any compact space X whose square X × X contains no uncountable discrete subsets.
Publisher
Canadian Mathematical Society
Subject
General Mathematics
Cited by
1 articles.
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