A remark on the normality of infinite products
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- by Keiko Chiba PDF
- Proc. Amer. Math. Soc. 105 (1989), 510-512 Request permission
Abstract:
In this note we shall prove the following: Suppose that all finite subproducts of a product space $X = \prod \nolimits _{\beta < \lambda } {{X_\beta }}$ are normal. If $X$ is $\lambda$-paracompact, then $X$ is normal. Here $\lambda$ stands for an infinite cardinal number.References
- Amer Bešlagić, Normality in products, Topology Appl. 22 (1986), no. 1, 71–82. MR 831182, DOI 10.1016/0166-8641(86)90078-7
- K. Morita, Paracompactness and product spaces, Fund. Math. 50 (1961/62), 223–236. MR 132525, DOI 10.4064/fm-50-3-223-236
- Keiô Nagami, Countable paracompactness of inverse limits and products, Fund. Math. 73 (1971/72), no. 3, 261–270. MR 301688, DOI 10.4064/fm-73-3-261-270
- Teodor C. Przymusiński, Products of normal spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 781–826. MR 776637
- 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
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 510-512
- MSC: Primary 54D15; Secondary 54B10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0933513-X
- MathSciNet review: 933513