Countable paracompactness of $F_ \sigma$-sets
HTML articles powered by AMS MathViewer
- by Phillip Zenor PDF
- Proc. Amer. Math. Soc. 55 (1976), 201-202 Request permission
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.References
- C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219–224. MR 43446, DOI 10.4153/cjm-1951-026-2
- Miroslaw Katětov, Complete normality of Cartesian products, Fund. Math. 35 (1948), 271–274. MR 27501, DOI 10.4064/fm-35-1-271-274
- K. Morita, Paracompactness and product spaces, Fund. Math. 50 (1961/62), 223–236. MR 132525, DOI 10.4064/fm-50-3-223-236
- Phillip Zenor, Countable paracompactness in product spaces, Proc. Amer. Math. Soc. 30 (1971), 199–201. MR 279769, DOI 10.1090/S0002-9939-1971-0279769-7
- Phillip Zenor, On countable paracompactness and normality, Prace Mat. 13 (1969), 23–32. MR 0248724
Additional Information
- © Copyright 1976 American Mathematical Society
- 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