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Products of Weak P-Spaces and K-Analytic Spaces

Part of: Maps and general types of spaces defined by maps Basic constructions

Published online by Cambridge University Press:  21 December 2009

Kaori Yamazaki
Kaori Yamazaki
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305–8571, Japan.
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Abstract

Let κ be an infinite cardinal. Okuyama showed that the product space X ×i Y of a paracompact weak P (ω)-space X and a K-analytic space Y is paracompact. In this paper, by using the notion of κ-K-analytic spaces which is basically defined by Hansell, Jayne and Rogers, the above result is extended and some other results are given related to normality, collectionwise normality and covering properties on products. An answer to a question of Okuyama and Watson is also given, as well as some applications to extensions of continuous functions on these products.

MSC classification

Secondary: 54B10: Product spaces 54C20: Extension of maps
Type
Research Article
Information
Mathematika , Volume 54 , Issue 1-2 , December 2007 , pp. 67 - 81
Copyright
Copyright © University College London 2007

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References

1Alò, R. A. and Shapiro, H. L., Normal Topological Spaces. Cambridge University Press (Cambridge, 1974).Google Scholar
2Balogh, Z. T., Nonshrinking open covers and K. Morita's third conjecture. Topology and its Appl. 84 (1998), 185–198.CrossRefGoogle Scholar
3Balogh, Z. T., Nonshrinking open covers and K. Morita's duality conjectures. Topology and its Appl. 115 (2001), 333–341.CrossRefGoogle Scholar
4Blair, R. L., A cardinal generalization of z-embedding. In Rings of Continuous Functions, Lecture Notes in Pure Appl. Math. 95, Marcel Dekker Inc. (1985), 7–78.Google Scholar
5Burke, D. K., Covering properties. In Handbook of Set-Theoretic Topology (ed. Kunen, K. and Vaughan, J. E.), North-Holland (Amsterdam, 1984), 347–422.CrossRefGoogle Scholar
6Burke, D. K. and Pol, R., Products of Michael spaces and completely metrizable spaces. Proc. Amer. Math. Soc. 129 (2001), 1535–1544.CrossRefGoogle Scholar
7Engelking, R., General Topology. Heldermann Verlag (Berlin, 1989).Google Scholar
8Gutev, V. and Ohta, H., Does C *-embedding imply C-embedding in the realm of products with a non-discrete metric factor?. Fund. Math. 163 (2000), 241–265.CrossRefGoogle Scholar
9Hansell, R. W., Jayne, J. E. and Rogers, C. A., K-analytic sets. Mathematika 30 (1983), 189–221. (Corrigenda et addenda, Mathematika 31 (1984), 28–32.)CrossRefGoogle Scholar
10Hoshina, T., Extensions of mappings, II. In Topics in General Topology (ed. Morita, K. and Nagata, J.), North-Holland (1989), 41–80.CrossRefGoogle Scholar
11Lutzer, D. J., Another property of the Sorgenfrey Line. Compositio Math. 24 (1972), 359–363.Google Scholar
12Mizokami, T., Metacompactness and subparacompactness of product spaces. J. Math. Soc. Japan 31 (1979), 263–272.CrossRefGoogle Scholar
13Morita, K., Products of normal spaces with metric spaces, II. Sci. Rep. Tokyo Kyoiku Daigaku A 8 (1963), 87–92.Google Scholar
14Morita, K., Products of normal spaces with metric spaces. Math. Ann. 154 (1964), 365–382.CrossRefGoogle Scholar
15Morita, K., Products of normal spaces with complete metric spaces. Q. and A. in Gen. Topology 14 (1996), 71–72.Google Scholar
16Nagami, K., Σ-spaces. Fund. Math. 65 (1969), 169–192.CrossRefGoogle Scholar
17Ohta, H., Extension properties and the Niemytzki plane. Appl. Gen. Topology 1 (2000), 45–60.CrossRefGoogle Scholar
18Okuyama, A., Note on paracompactness in product spaces. Topology Proc. 16 (1991), 119–124.Google Scholar
19Okuyama, A. and Watson, S., Note on hereditary normality of product spaces. Topology and its Appl. 82 (1998), 369–375.CrossRefGoogle Scholar
20Rogers, C. A. and Jayne, J. E., K-analytic sets. In Analytic Sets, Part I, Academic Press (1980), 1–181.Google Scholar
21Rudin, M. E. and Starbird, M., Products with a metric factor. Gen. Topology Appl. 5 (1975), 235–248.CrossRefGoogle Scholar
22Stone, A. H., Absolute F σ-spaces. Proc. Amer. Math. Soc. 13 (1962), 495–499.Google Scholar
23Vaughan, J. E., Nonnormal products of ωμ-metrizable spaces. Proc. Amer. Math. Soc. 51 (1975), 203–208.Google Scholar
24Yajima, Y., Special refinements and their applications on products. Topology and its Appl. 104 (2000), 293–308.CrossRefGoogle Scholar
25Yamazaki, K., Normality and collectionwise normality on product spaces. Topology Proc. 22 (1997), 383–392.Google Scholar
26Yamazaki, K., Normality and collectionwise normality on product spaces, II. Tsukuba J. Math. 22 (1998), 783–793.CrossRefGoogle Scholar
27Yamazaki, K., A cardinal generalization of C *-embedding and its applications. Topology and its Appl. 108 (2000), 137–156.CrossRefGoogle Scholar
28Yamazaki, K., C *-embeddings and P-or M-embeddings on product spaces. Houston J. Math. 27 (2001), 861–872.Google Scholar