The Hewitt realcompactification of products

Ohta, Haruto

doi:10.1090/S0002-9947-1981-0594414-X

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: For a completely regular Hausdorff space , $\upsilon X$ denotes the Hewitt realcompactification of . Given a topological property $\mathcal{P}$ of spaces, our interest is in characterizing the class $\mathcal{R}(\mathcal{P})$ of all spaces such that $\upsilon (X \times Y) = \upsilon X \times \upsilon Y$ holds for each $\mathcal{P}$ -space . 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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