The normality of ∑-products and the perfect κ-normality of Cartesian products

Yukinobu YAJIMA

doi:10.2969/jmsj/03640689

Yukinobu YAJIMA

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 4 Pages 689-699

DOI https://doi.org/10.2969/jmsj/03640689

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Published: 1984 Received: March 03, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) A. V. Arhangel'skii, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys, 33 (1978), 33-96.
2) R. L. Blair, Spaces in which special sets are z-embedded, Canad. J. Math., 28 (1976), 673-690.
3) H. H. Corson, Normality in subsets of product spaces, Amer. J. Math., 81 (1959), 785-796.
4) S. P. Gul'ko, On the properties of subsets of ∑-products, Soviet Math. Dokl., 18 (1977), 1438-1442.
5) B. S. Klebanov, Remarks on subsets of Cartesian products of metric spaces, Comment. Math. Univ. Carolinae, 23 (1982), 767-784.
6) A. P. Kombarov, On ∑-products of topological spaces, Soviet Math. Dokl., 12 (1971), 1101-1104.
7) A. P. Kombarov, On the normality of ∑_m-products, Soviet Math. Dokl., 14 (1973), 1050-1054.
8) A. P. Kombarov, On tightness and normality of ∑-products, Soviet Math. Dokl., 19 (1978), 403-407.
9) V. I. Malyhin, On tightness and Souslin number in exp X and in a product of spaces, Soviet Math. Dokl., 13 (1972), 496-499.
10) K. Morita, Products of normal spaces with metric spaces, Math. Ann., 154 (1964), 365-382.
11) K. Nagami, ∑-spaces, Fund. Math., 65 (1969), 169-192.
12) K. Nagami, Countable paracompactness of inverse limits and products, Fund. Math., 73 (1972), 261-270.
13) A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 9 (1967), 236-254.
14) R. Pol and E. Pol, Remarks on Cartesian products, Fund. Math., 93 (1976), 57-69.
15) M. E. Rudin, Book Review, Bull. Amer. Math. Soc., 84 (1978), 271-272.
16) V. E. Šcepin, On topological products, groups and a new class of spaces more general than metric spaces, Soviet Math. Dokl., 17 (1976), 152-155.
17) V. E. Šcepin, Topology of limit spaces of uncountable inverse spectra, Russian Math. Surveys, 31 (1976), 155-191.
18) R. Telgársky, A characterization of P-spaces, Proc. Japan Acad., 51 (1975), 802-807.
19) T. Terada, Note on z-, C^*-, and C-embedding, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 13 (1975), 129-132.
20) M. G. Tkacenko, The notion of o-tightness and C-embedded subspaces of products, Topology and Appl., 15 (1983), 93-98.
21) Y. Yajima, On ∑-products of ∑-spaces, Fund. Math., to appear.

Right : [1] A. V. Arhangel'skii, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys, 33 (1978), 33-96.
[2] R. L. Blair, Spaces in which special sets are z-embedded, Canad. J. Math., 28 (1976), 673-690.
[3] H. H. Corson, Normality in subsets of product spaces, Amer. J. Math., 81 (1959), 785-796.
[4] S. P. Gul'ko, On the properties of subsets of ∑-products, Soviet Math. Dokl., 18 (1977), 1438-1442.
[5] B. S. Klebanov, Remarks on subsets of Cartesian products of metric spaces, Comment. Math. Univ. Carolinae, 23 (1982), 767-784.
[6] A. P. Kombarov, On ∑-products of topological spaces, Soviet Math. Dokl., 12 (1971), 1101-1104.
[7] A. P. Kombarov, On the normality of ∑_m-products, Soviet Math. Dokl., 14 (1973), 1050-1054.
[8] A. P. Kombarov, On tightness and normality of ∑-products, Soviet Math. Dokl., 19 (1978), 403-407.
[9] V. I. Malyhin, On tightness and Souslin number in exp X and in a product of spaces, Soviet Math. Dokl., 13 (1972), 496-499.
[10] K. Morita, Products of normal spaces with metric spaces, Math. Ann., 154 (1964), 365-382.
[11] K. Nagami, ∑-spaces, Fund. Math., 65 (1969), 169-192.
[12] K. Nagami, Countable paracompactness of inverse limits and products, Fund. Math., 73 (1972), 261-270.
[13] A. Okuyama, Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 9 (1967), 236-254.
[14] R. Pol and E. Pol, Remarks on Cartesian products, Fund. Math., 93 (1976), 57-69.
[15] M. E. Rudin, Book Review, Bull. Amer. Math. Soc., 84 (1978), 271-272.
[16] V. E. Šcepin, On topological products, groups and a new class of spaces more general than metric spaces, Soviet Math. Dokl., 17 (1976), 152-155.
[17] V. E. Šcepin, Topology of limit spaces of uncountable inverse spectra, Russian Math. Surveys, 31 (1976), 155-191.
[18] R. Telgársky, A characterization of P-spaces, Proc. Japan Acad., 51 (1975), 802-807.
[19] T. Terada, Note on z-, C-, and C-embedding, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 13 (1975), 129-132.
[20] M. G. Tkacenko, The notion of o-tightness and C-embedded subspaces of products, Topology and Appl., 15 (1983), 93-98.
[21] Y. Yajima, On ∑-products of ∑-spaces, Fund. Math., to appear.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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