A metric characterizing Čech dimension zero

Author:

Broughan K. A.

Abstract

In this paper we prove the following: a metrizable space ( X , τ ) (X,\tau ) has (Čech) dimension zero if and only if there is a metric for X X , generating the topology τ \tau , taking values in some subset of the nonnegative real numbers with 0 as its only cluster point.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. On a metric that characterizes dimension;de Groot, J.;Canadian J. Math.,1957

2. On a relation between dimension and metrization;Nagata, Jun-iti;Proc. Japan Acad.,1956

3. Two theorems for the 𝑛-dimensionality of metric spaces;Nagata, Jun-iti;Compositio Math.,1963

4. A metric characterization of zero-dimensional spaces;Janoš, Ludvík;Proc. Amer. Math. Soc.,1972

5. K. Broughan and M. Schroder, Variations on a metric theme, Report #14, Univ. of Waikato Research, 1972.

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