A characterization for the products of $k$- and $\aleph _{0}$-spaces and related results
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- by Yoshio Tanaka
- Proc. Amer. Math. Soc. 59 (1976), 149-155
- DOI: https://doi.org/10.1090/S0002-9939-1976-0415580-6
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Abstract:
E. Michael introduced the notion of ${\aleph _0}$-spaces and characterized spaces which are both $k$-spaces and ${\aleph _0}$-spaces (or, briefly, $k$-and-${\aleph _0}$-spaces) as being precisely the quotient images of separable metric spaces. The purpose of this paper is to give a necessary and sufficient condition for the product of two $k$-and-${\aleph _0}$-spaces to be a $k$-and-${\aleph _0}$-space. Moreover, as related matters, we shall consider the products of $k$-spaces having other properties.References
- A. V. Arhangel′skiĭ, Bicompact sets and the topology of spaces., Trudy Moskov. Mat. Obšč. 13 (1965), 3–55 (Russian). MR 0195046
- Carlos J. R. Borges, On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16. MR 188982, DOI 10.2140/pjm.1966.17.1
- D. E. Cohen, Spaces with weak topology, Quart. J. Math. Oxford Ser. (2) 5 (1954), 77–80. MR 63043, DOI 10.1093/qmath/5.1.77
- S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, DOI 10.4064/fm-57-1-107-115
- E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc. 8 (1957), 822–828. MR 87079, DOI 10.1090/S0002-9939-1957-0087079-9
- E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173–176. MR 177396, DOI 10.1007/BF02759940
- E. Michael, $\aleph _{0}$-spaces, J. Math. Mech. 15 (1966), 983–1002. MR 0206907
- Ernest Michael, Bi-quotient maps and Cartesian products of quotient maps, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 287–302 vii (1969) (English, with French summary). MR 244964, DOI 10.5802/aif.301
- E. A. Michael, A quintuple quotient quest, General Topology and Appl. 2 (1972), 91–138. MR 309045, DOI 10.1016/0016-660X(72)90040-2
- John Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272–284. MR 77122, DOI 10.2307/1969609
- Kiiti Morita, On decomposition spaces of locally compact spaces, Proc. Japan Acad. 32 (1956), 544–548. MR 85495
- Kiiti Morita, Products of normal spaces with metric spaces, Math. Ann. 154 (1964), 365–382. MR 165491, DOI 10.1007/BF01362570
- Keiô Nagami, Dimension for $\sigma$-metric spaces, J. Math. Soc. Japan 23 (1971), 123–129. MR 287521, DOI 10.2969/jmsj/02310123
- 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
- Paul O’Meara, A metrization theorem, Math. Nachr. 45 (1970), 69–72. MR 279768, DOI 10.1002/mana.19700450103
- Paul O’Meara, On paracompactness in function spaces with the compact-open topology, Proc. Amer. Math. Soc. 29 (1971), 183–189. MR 276919, DOI 10.1090/S0002-9939-1971-0276919-3
- Frank Siwiec, Sequence-covering and countably bi-quotient mappings, General Topology and Appl. 1 (1971), no. 2, 143–154. MR 288737, DOI 10.1016/0016-660X(71)90120-6
- Yoshio Tanaka, On quasi-$k$-spaces, Proc. Japan Acad. 46 (1970), 1074–1079. MR 296887, DOI 10.2183/pjab1945.46.1074
- Yoshio Tanaka, Products of sequential spaces, Proc. Amer. Math. Soc. 54 (1976), 371–375. MR 397665, DOI 10.1090/S0002-9939-1976-0397665-6
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 149-155
- MSC: Primary 54E35; Secondary 54B10, 54D50
- DOI: https://doi.org/10.1090/S0002-9939-1976-0415580-6
- MathSciNet review: 0415580