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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Four metric conditions characterizing Čech dimension zero

Author: Kevin Broughan
Journal: Proc. Amer. Math. Soc. 64 (1977), 176-178
MSC: Primary 54E35; Secondary 54F45
MathSciNet review: 0515020
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Abstract: If (X,d) is a metric space let $ {d_x}(y) = d(x,y)$. It is proved that if each x in X has a neighbourhood P with $ {d_x}(P)$ not dense in any neighbourhood of 0 in $ [0,\infty )$ then Ind $ X = 0$. This metric condition characterizes metrizable spaces which have Čech dimension zero. Three other metric characterizations are given.

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PII: S 0002-9939(1977)0515020-3
Keywords: Metric spaces, Čech dimension zero
Article copyright: © Copyright 1977 American Mathematical Society