On collectionwise normality of product spaces. I

Chiba, Keiko

doi:10.1090/S0002-9939-1984-0746107-1

On collectionwise normality of product spaces. I
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by Keiko Chiba

Proc. Amer. Math. Soc. 91 (1984), 649-652

DOI: https://doi.org/10.1090/S0002-9939-1984-0746107-1

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Abstract:

In this paper the following result will be obtained: Let $X$ be a collectionwise normal $\Sigma$-space (in the sense of Nagami [9]) and $Y$ a paracompact first countable $P$-space (in the sense of Morita [8]). Then $X \times Y$ is collectionwise normal.

References

R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175–186. MR 43449, DOI 10.4153/cjm-1951-022-3
Keiko Chiba, On products of normal spaces, Rep. Fac. Sci. Shizuoka Univ. 9 (1974), 1–11. MR 370495
Tôru Chiba and Keiko Chiba, A note on normality of product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 12 (1974), 165–173. MR 377814
M. Katětov, Extension of locally finite coverings, Colloq. Math. 6 (1958), 145–151 (Russian). MR 103450

On the product of normal spaces. Uniformities on

-products

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E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3
E. A. Michael, A quintuple quotient quest, General Topology and Appl. 2 (1972), 91–138. MR 309045
Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365–382. MR 165491, DOI 10.1007/BF01362570
Keiô Nagami, $\Sigma$-spaces, Fund. Math. 65 (1969), 169–192. MR 257963, DOI 10.4064/fm-65-2-169-192
Akihiro Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 9 (1968), 236–254 (1968). MR 230283
R. Pol, A perfectly normal locally metrizable non-paracompact space, Fund. Math. 97 (1977), no. 1, 37–42. MR 464178, DOI 10.4064/fm-139-1-37-47
R. H. Sorgenfrey, On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631–632. MR 20770, DOI 10.1090/S0002-9904-1947-08858-3
Hisahiro Tamano, On compactifications, J. Math. Kyoto Univ. 1 (1961/62), 161–193. MR 142096, DOI 10.1215/kjm/1250525055
Yukinobu Yajima, Topological games and products. I, Fund. Math. 113 (1981), no. 2, 141–153. MR 640619, DOI 10.4064/fm-113-2-141-153