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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0288739-5
MathSciNet review: 0288739
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0288739-5
Keywords: Rigid metric, strongly rigid metric, eventually strongly rigid, zero-dimensional
Article copyright: © Copyright 1972 American Mathematical Society