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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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  • [1] J. de Groot, On a metric that characterizes dimension, Canad. J. Math. 9 (1957), 511-514. MR 19, 874. MR 0090804 (19:874f)
  • [2] J. Nagata, On a relation between dimension and metrization, Proc. Japan Acad. 32 (1956), 237-240. MR 19, 156. MR 0086284 (19:156e)
  • [3] -, Two theorems for the $ n$-dimensionality of metric spaces, Compositio Math. 15 (1963), 227-237. MR 29 #1617. MR 0164320 (29:1617)
  • [4] L. Janos, A metric characterization of zero-dimensional spaces, Proc. Amer. Math. Soc. 31 (1972), 268-270. MR 0288739 (44:5935)
  • [5] K. Broughan and M. Schroder, Variations on a metric theme, Report #14, Univ. of Waikato Research, 1972.
  • [6] K. Morita, Normal families and dimension theory for metric spaces, Math. Ann. 128 (1954), 350-362. MR 16, 501. MR 0065906 (16:501h)

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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

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