Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [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 0180954 (31:5184)
  • [4] J. de Groot, Discrete subspaces of Hausdorff spaces, Bull. Acad. Polon. Sci. Sér, Sci. Math. Astronom. 13 (1965), 537-544. MR 0210061 (35:956)
  • [5] I. Juhász, Cardinal functions in topology, Math. Centrum, Amsterdam, 1971. MR 0340021 (49:4778)
  • [6] D. J. Lutzer, Semimetrizable and stratifiable spaces, Topology Appl. 1 (1971), 43-48. MR 0296893 (45:5952)
  • [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 0177396 (31:1659)
  • [9] -, A quintuple quotient quest, Topology Appl. 2 (1972), 91-138. MR 0309045 (46:8156)
  • [10] E. Michael, R. C. Olson and F. Siwiec, $ A$-spaces and countably bi-quotient maps, Dissertationes Math. (Rozprawy Mat.) 133 (1976), 4-43. MR 0418023 (54:6067)
  • [11] K. Morita and S. Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), 10-14. MR 0087077 (19:299a)
  • [12] K. Nagami, $ \Sigma $-spaces, Fund. Math. 65 (1969), 169-192. MR 0257963 (41:2612)
  • [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 0087078 (19:299b)
  • [15] Y. Tanaka, Closed maps on metric spaces, Topology Appl. 11 (1980), 87-92. MR 550875 (82k:54017)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25, 54C10, 54D20, 54D55

Retrieve articles in all journals with MSC: 54A25, 54C10, 54D20, 54D55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0727260-2
Keywords: Closed map, strongly collectionwise Hausdorff, $ \alpha $-compact, $ \alpha $-Lindelöf, sequential space, character
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society