A metric characterizing Čech dimension zero

Broughan, K. A.

doi:10.1090/S0002-9939-1973-0314012-3

A metric characterizing Čech dimension zero
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Proc. Amer. Math. Soc. 39 (1973), 437-440 Request permission

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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Variations on a metric theme

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