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Countable paracompactness of $ F\sb \sigma$-sets


Author: Phillip Zenor
Journal: Proc. Amer. Math. Soc. 55 (1976), 201-202
MSC: Primary 54D20
DOI: https://doi.org/10.1090/S0002-9939-1976-0402685-9
MathSciNet review: 0402685
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Abstract: If each $ {F_\sigma }$-set in $ X \times Y$ is countably paracompact, then either $ X$ is normal or no countable discrete subset of $ Y$ has a limit point. It follows that, for each cardinal number $ \mathfrak{m}$, there is an $ \mathfrak{m}$-paracompact space containing a noncountably paracompact $ {F_\sigma }$-subset.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0402685-9
Article copyright: © Copyright 1976 American Mathematical Society

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