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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Four metric conditions characterizing Čech dimension zero
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by Kevin Broughan PDF
Proc. Amer. Math. Soc. 64 (1977), 176-178 Request permission

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.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 176-178
  • MSC: Primary 54E35; Secondary 54F45
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0515020-3
  • MathSciNet review: 0515020