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Metrization of spaces having Čech dimension zero

Published online by Cambridge University Press:  17 April 2009

K.A. Broughan
K.A. Broughan
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand.
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Abstract

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A metrizable topological space has a metric taking values in a closed subset of the real numbers having Čech dimension zero if and only if the space itself has Čech dimension zero. We call a development D = {Dn} for a topological space (X, T) a sieve for X if the sets in each Dn are pairwise disjoint. Then a Hausdorff topological space (X, T) has a compatible metric taking values in a closed subset of the real numbers having Čech dimension zero if and only if there exists a sieve for X.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 2 , October 1973 , pp. 161 - 168
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Broughan, K.A., “A metric characterizing Čech dimension zero”, Proc. Amer. Math. Soc. (to appear).Google Scholar
[2]Broughan, K.A., “Clopen-paracompact topological spaces”, (to appear).Google Scholar
[3]Broughan, K.A., “Dimension zero”, (to appear).Google Scholar
[4]Kuratowski, Casimir, “Quelques problèmes concernant les espaces métriques non-séparables”, Fund. Math. 25 (1935), 534–545.Google Scholar
[5]Morita, Kiiti, “A condition for the metrizability of topological spaces and for n–dimensionality”, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 5 (1955), 33–36.Google Scholar
[6]Roy, Prabir, “Failure of equivalence of dimension concepts for metric spaces”, Bull. Amer. Math. Soc. 68 (1968), 609–613.Google Scholar