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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The Hewitt realcompactification of products

Author: Haruto Ohta
Journal: Trans. Amer. Math. Soc. 263 (1981), 363-375
MSC: Primary 54D60; Secondary 54B10
MathSciNet review: 594414
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Abstract: For a completely regular Hausdorff space $ X$, $ \upsilon X$ denotes the Hewitt realcompactification of $ X$. Given a topological property $ \mathcal{P}$ of spaces, our interest is in characterizing the class $ \mathcal{R}(\mathcal{P})$ of all spaces $ X$ such that $ \upsilon (X \times Y) = \upsilon X \times \upsilon Y$ holds for each $ \mathcal{P}$-space $ Y$. In the present paper, we obtain such characterizations in the case that $ \mathcal{P}$ is locally compact and in the case that $ \mathcal{P}$ is metrizable.

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PII: S 0002-9947(1981)0594414-X
Keywords: Hewitt realcompactification, product space, locally compact space, metrizable space, weak $ {\text{c}}{{\text{b}}^ \ast }$-space, pseudo- $ \mathfrak{m}$-compact space, quotient map, perfect map, $ C$-embedding, absolute, nonmeasurable cardinal, $ D(\mathfrak{m})$-expandable family
Article copyright: © Copyright 1981 American Mathematical Society