Countable paracompactness in product spaces
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- by Phillip Zenor PDF
- Proc. Amer. Math. Soc. 30 (1971), 199-201 Request permission
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.References
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- Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502
- Phillip Zenor, On countable paracompactness and normality, Prace Mat. 13 (1969), 23–32. MR 0248724
Additional Information
- © Copyright 1971 American Mathematical Society
- 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