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On collectionwise normality of product spaces. II


Author: Keiko Chiba
Journal: Proc. Amer. Math. Soc. 91 (1984), 653-657
MSC: Primary 54B10; Secondary 54D15
DOI: https://doi.org/10.1090/S0002-9939-1984-0746108-3
MathSciNet review: 746108
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the following results will be obtained. (1) Let $ X$ be a closed image of a normal $ M$-space and $ Y$ a paracompact first countable $ P$-space. If $ X \times Y$ is normal, then $ X \times Y$ is collectionwise normal. (2) Let $ X$ be a collectionwise normal space and $ Y$ a $ \sigma $-locally compact paracompact space. If $ X \times Y$ is normal, then $ X \times Y$ is collectionwise normal.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0746108-3
Keywords: Product space, normal, collectionwise normal, paracompact, first countable, $ M$-space, $ P$-space, $ \sigma $-locally compact
Article copyright: © Copyright 1984 American Mathematical Society

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