Geodesic
The Normality in Products with a Countably Compact Factor
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 245-251

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1998-035-x
Mots-clés : 54B19, 54D15, 54D20 
Yang, Lecheng. The Normality in Products with a Countably Compact Factor. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 245-251. doi: 10.4153/CMB-1998-035-x
@article{10_4153_CMB_1998_035_x,
     author = {Yang, Lecheng},
     title = {The {Normality} in {Products} with a {Countably} {Compact} {Factor}},
     journal = {Canadian mathematical bulletin},
     pages = {245--251},
     year = {1998},
     volume = {41},
     number = {2},
     doi = {10.4153/CMB-1998-035-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-035-x/}
}
TY  - JOUR
AU  - Yang, Lecheng
TI  - The Normality in Products with a Countably Compact Factor
JO  - Canadian mathematical bulletin
PY  - 1998
SP  - 245
EP  - 251
VL  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-035-x/
DO  - 10.4153/CMB-1998-035-x
ID  - 10_4153_CMB_1998_035_x
ER  - 
%0 Journal Article
%A Yang, Lecheng
%T The Normality in Products with a Countably Compact Factor
%J Canadian mathematical bulletin
%D 1998
%P 245-251
%V 41
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-035-x/
%R 10.4153/CMB-1998-035-x
%F 10_4153_CMB_1998_035_x

[1] 1. Alas, O. T., On a characterization of collectionwise normality, Canad.Math. Bull. 14 (1971), 13–15. Google Scholar

[2] 2. Bešlagic, A., Normality in products, Topology Appl. 22 (1986), 71–82. Google Scholar

[3] 3. Chiba, K., On products of normal spaces, Rep. Fac. Sci. Shizuoka Univ. 9 (1974), 1–11. Google Scholar

[4] 4. Creede, G. D., Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970), 47–54. Google Scholar

[5] 5. Dieudonné, J., Un critére de normalité pour les espaces produits, Colloq. Math. 6 (1958), 29–32. Google Scholar

[6] 6. Engelking, R., General Topology, Haldermann Verlin, 1989. Google Scholar

[7] 7. Gruenhage, G., Nogura, T. and Purisch, S., Normality of X × ω1, Topology Appl. 39 (1991), 263–275. Google Scholar

[8] 8. Hoshina, T., Products of normal spaces with Lašnev spaces, Fund. Math. 124 (1984), 143–153. Google Scholar

[9] 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] 10. Kemoto, N. and Yajima, Y., Orthocompactness and normality of products with a cardinal factor, Topology Appl. 49 (1993), 141–148. Google Scholar

[11] 11. Kombarov, A. P., On the product of normal spaces.Uniformities of Σ-products, Soviet Math.Dokl. 13 (1972), 1068–1071. Google Scholar

[12] 12. Morita, K., Paracompactness and product spaces, Fund Math. 50(1961/62), 223–236. Google Scholar

[13] 13. Nagami, K., Countable paracompactness of inverse limits and products, Fund. Math. 73 (1972), 261–270. Google Scholar

[14] 14. Nogura, T., Tightness of compactHausdorff spaces and normality of products, J.Math. Soc. Japan 28 (1976), 360–362. Google Scholar

[15] 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] 16. Rudin, M. E. and Starbird, M., Products with a metric factor, General Topology Appl. 5 (1975), 235–248. Google Scholar

[17] 17. Stone, A. H., Paracompactness and product spaces, Bull. Amer.Math. Soc. 54 (1948), 977–982. Google Scholar

[18] 18. Yajima, Y., Subnormality of X × κ and Σ-products, Topology Appl. 54 (1993), 111–122. Google Scholar

[19] 19. Yang, L., Countable paracompactness of Σ-products Proc. Amer. Math. Soc., 122 (1994), 949–956. Google Scholar

[20] 20. Zenor, P., Countable paracompactness in product spaces, Proc. Amer. Math. Soc. 30 (1971), 199–201. Google Scholar

Cité par Sources :