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Proceedings of the American Mathematical Society

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



A metric characterization of zero-dimensional spaces

Author: Ludvík Janoš
Journal: Proc. Amer. Math. Soc. 31 (1972), 268-270
MathSciNet review: 0288739
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Abstract | References | Additional Information

Abstract: It is shown that a nonempty separable metrizable space $ X$ is zero-dimensional if and only if there exists a metric $ \rho $ on $ X$, inducing the given topology of $ X$ and such that all nonzero distances $ \rho (x,y)$ are mutually different.

References [Enhancements On Off] (What's this?)

  • [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)

Additional Information

Keywords: Rigid metric, strongly rigid metric, eventually strongly rigid, zero-dimensional
Article copyright: © Copyright 1972 American Mathematical Society

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