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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

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