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Proceedings of the American Mathematical Society

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

 
 

 

Products of $ M$-spaces


Author: C. Bandy
Journal: Proc. Amer. Math. Soc. 45 (1974), 426-430
MSC: Primary 54E99
DOI: https://doi.org/10.1090/S0002-9939-1974-0346759-8
MathSciNet review: 0346759
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Abstract: The author associates with each pair $ X,Y$ of $ M$-spaces such that $ X \times Y$ is not an $ M$-space, a pair of countably compact closed subspaces $ A \subset X,B \subset Y$ such that $ A \times B$ is not countably compact, and for each pair $ A,B$ of countably compact spaces whose product is not countably compact, there is a pair of $ M$-spaces $ S,T$ (in fact, $ S$ and $ T$ ate countably compact) such that $ S \times T$ is not an $ M$-space and such that $ A$ and $ B$ are closed subspaces of $ S$ and $ T$ respectively.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0346759-8
Keywords: $ M$-space, normal sequence, $ M$-sequence
Article copyright: © Copyright 1974 American Mathematical Society

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