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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Countable paracompactness in product spaces


Author: Phillip Zenor
Journal: Proc. Amer. Math. Soc. 30 (1971), 199-201
MSC: Primary 54.50
DOI: https://doi.org/10.1090/S0002-9939-1971-0279769-7
MathSciNet review: 0279769
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Abstract: The main purpose of this paper is to show that $ {X^\omega }$ is normal if and only if (1) $ {X^n}$ is normal for each n, and (2) $ {X^\omega }$ is countably paracompact. Furthermore, $ {X^\omega }$ is perfectly normal if and only if $ {X^\omega }$ is hereditarily countably paracompact. Also, the compact Hausdorff space X is metrizable if and only if $ {X^3}$ is hereditarily countably paracompact.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0279769-7
Keywords: Product spaces, normality, countable paracompactness
Article copyright: © Copyright 1971 American Mathematical Society