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The Normality in Products with a Countably Compact Factor

Published online by Cambridge University Press:  20 November 2018

Lecheng Yang
Lecheng Yang*
Affiliation:
Institute of Mathematics University of Tsukuba Tsukuba-city 305 Japan
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Abstract

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It is known that the product ${{\omega }_{1}}\times X$ of ${{\omega }_{1}}$ with an ${{M}_{1}}$-space may be non-normal. In this paper we prove that the product $\kappa \times X$ of an uncountable regular cardinal κ with a paracompact semi-stratifiable space is normal iff it is countably paracompact. We also give a sufficient condition under which the product of a normal space with a paracompact space is normal, from which many theorems involving such a product with a countably compact factor can be derived.

Keywords

54B1954D1554D20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 2 , 01 June 1998 , pp. 245 - 251
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Alas, O. T., On a characterization of collectionwise normality, Canad.Math. Bull. 14 (1971), 13–15.Google Scholar
2. Bešlagic, A., Normality in products, Topology Appl. 22 (1986), 71–82.Google Scholar
3. Chiba, K., On products of normal spaces, Rep. Fac. Sci. Shizuoka Univ. 9 (1974), 1–11.Google Scholar
4. Creede, G. D., Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47–54.Google Scholar
5. Dieudonné, J., Un critére de normalité pour les espaces produits, Colloq. Math. 6 (1958), 29–32.Google Scholar
6. Engelking, R., General Topology, Haldermann Verlin, 1989.Google Scholar
7. Gruenhage, G., Nogura, T. and Purisch, S., Normality of X × ω1, Topology Appl. 39 (1991), 263–275.Google Scholar
8. Hoshina, T., Products of normal spaces with Lašnev spaces, Fund. Math. 124 (1984), 143–153.Google Scholar
9. Hoshina, T., Normality of product spaces II, Topics in General Topology (K. Morita and J. Nagata, eds.) North-Holland, Amsterdam, 1989.Google Scholar
10. Kemoto, N. and Yajima, Y., Orthocompactness and normality of products with a cardinal factor, Topology Appl. 49 (1993), 141–148.Google Scholar
11. Kombarov, A. P., On the product of normal spaces.Uniformities of Σ-products, Soviet Math.Dokl. 13 (1972), 1068–1071.Google Scholar
12. Morita, K., Paracompactness and product spaces, Fund Math. 50(1961/62), 223–236.Google Scholar
13. Nagami, K., Countable paracompactness of inverse limits and products, Fund. Math. 73 (1972), 261–270.Google Scholar
14. Nogura, T., Tightness of compactHausdorff spaces and normality of products, J.Math. Soc. Japan 28 (1976), 360–362.Google Scholar
15. Przymusiński, T. C., Products of normal spaces, Handbook of Set Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, Amsterdam, 1984.Google Scholar
16. Rudin, M. E. and Starbird, M., Products with a metric factor, General Topology Appl. 5 (1975), 235–248.Google Scholar
17. Stone, A. H., Paracompactness and product spaces, Bull. Amer.Math. Soc. 54 (1948), 977–982.Google Scholar
18. Yajima, Y., Subnormality of X × κ and Σ-products, Topology Appl. 54 (1993), 111–122.Google Scholar
19. Yang, L., Countable paracompactness of Σ-products Proc. Amer. Math. Soc., 122 (1994), 949–956.Google Scholar
20. Zenor, P., Countable paracompactness in product spaces, Proc. Amer. Math. Soc. 30 (1971), 199–201.Google Scholar