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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A metric characterizing Čech dimension zero


Author: K. A. Broughan
Journal: Proc. Amer. Math. Soc. 39 (1973), 437-440
MSC: Primary 54F45; Secondary 54E35
DOI: https://doi.org/10.1090/S0002-9939-1973-0314012-3
MathSciNet review: 0314012
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Abstract: In this paper we prove the following: a metrizable space $ (X,\tau )$ has (Čech) dimension zero if and only if there is a metric for $ X$, generating the topology $ \tau $, taking values in some subset of the nonnegative real numbers with 0 as its only cluster point.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0314012-3
Keywords: Metric spaces, Čech dimension zero
Article copyright: © Copyright 1973 American Mathematical Society