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Proceedings of the American Mathematical Society

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

 

 

On the topological completion of $ M$-space products


Author: A. K. Steiner
Journal: Proc. Amer. Math. Soc. 29 (1971), 617-620
MSC: Primary 54.53
MathSciNet review: 0282339
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Abstract: Using the continuum hypothesis, an example is given of two countably compact spaces X and Y such that $ X \times Y$ is an M-space, but is not countably compact. If $ \mu X$ denotes the completion of X with respect to its finest uniformity, the above example shows that $ \mu (X \times Y)$ is not necessarily equal to $ \mu X \times \mu Y$, even though $ X \times Y$ is an M-space.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0282339-8
Keywords: Countable compactness, M-spaces
Article copyright: © Copyright 1971 American Mathematical Society