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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
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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Keywords: Realcompact, $ \theta $-refinable
Article copyright: © Copyright 1973 American Mathematical Society