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Certain Subsets of Products of Metacompact Spaces and Subparacompact Spaces are Realcompact

Published online by Cambridge University Press:  20 November 2018

Phillip Zenor
Phillip Zenor*
Affiliation:
Auburn University, Auburn, Alabama
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We will say that a space X has property (*) if and only if each discrete subset of X is realcompact; i.e., the cardinality of each discrete subset of X is nonmeasurable. In [8], Shirota shows that a completely regular T1-space X is realcompact if and only if X has property (*) and X is complete with respect to some uniformity. In [7], Moran, using measure theoretic techniques, shows that any normal metacompact T1-space with property (*) is realcompact.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 825 - 829
Copyright
Copyright © Canadian Mathematical Society 1972

References

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