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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Certain subsets of products of $ \theta $-refinable spaces are realcompact


Author: Phillip Zenor
Journal: Proc. Amer. Math. Soc. 40 (1973), 612-614
MSC: Primary 54D60
DOI: https://doi.org/10.1090/S0002-9939-1973-0322812-9
MathSciNet review: 0322812
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Abstract: It is shown that the normal $ {T_1}$-space $ X$ is realcompact if and only if (a) each discrete subset of $ X$ is realcompact and (b) $ X$ can be embedded as a closed subset in the product of a collection of regular $ \theta $-refinable spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0322812-9
Keywords: Realcompact, $ \theta $-refinable
Article copyright: © Copyright 1973 American Mathematical Society