Closed maps and the character of spaces

Tanaka, Yoshio

doi:10.1090/S0002-9939-1984-0727260-2

Closed maps and the character of spaces

Author: Yoshio Tanaka
Journal: Proc. Amer. Math. Soc. 90 (1984), 327-332
MSC: Primary 54A25; Secondary 54C10, 54D20, 54D55
DOI: https://doi.org/10.1090/S0002-9939-1984-0727260-2
MathSciNet review: 727260
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give some necessary and sufficient conditions for the character of spaces to be preserved under closed maps.

[1] A. V. Arhangel'skiĭ, Some types of factor mappings, and the relations between classes of topological spaces, Soviet Math. Dokl. 4 (1963), 1726-1729.
[2] -, On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955.
[3] S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107–115. MR 180954, https://doi.org/10.4064/fm-57-1-107-115
[4] J. de Groot, Discrete subspaces of Hausdorff spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 537–544. MR 210061
[5] I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021
[6] D. J. Lutzer, Semimetrizable and stratifiable spaces, General Topology and Appl. 1 (1971), no. 1, 43–48. MR 296893
[7] V. I. Malyhin and B. E. Šapirovskiĭ, Martin's axiom and properties of topological spaces, Soviet Math. Dokl. 14 (1973), 1746-1751.
[8] E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173–176. MR 177396, https://doi.org/10.1007/BF02759940
[9] E. A. Michael, A quintuple quotient quest, General Topology and Appl. 2 (1972), 91–138. MR 309045
[10] E. Michael, R. C. Olson, and F. Siwiec, 𝐴-spaces and countably bi-quotient maps, Dissertationes Math. (Rozprawy Mat.) 133 (1976), 43. MR 0418023
[11] Kiiti Morita and Sitiro Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), 10–14. MR 87077
[12] Keiô Nagami, Σ-spaces, Fund. Math. 65 (1969), 169–192. MR 257963, https://doi.org/10.4064/fm-65-2-169-192
[13] D. V. Rančin, Tightness, sequentiality and closed coverings, Soviet Math. Dokl. 18 (1977), 196-200.
[14] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, https://doi.org/10.1090/S0002-9939-1956-0087078-6
[15] Yoshio Tanaka, Closed maps on metric spaces, Topology Appl. 11 (1980), no. 1, 87–92. MR 550875, https://doi.org/10.1016/0166-8641(80)90019-X