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Transactions of the American Mathematical Society

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The Hewitt realcompactification of products


Author: Haruto Ohta
Journal: Trans. Amer. Math. Soc. 263 (1981), 363-375
MSC: Primary 54D60; Secondary 54B10
DOI: https://doi.org/10.1090/S0002-9947-1981-0594414-X
MathSciNet review: 594414
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0594414-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

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