Advertisement

Lobachevskii Journal of Mathematics

, Volume 30, Issue 2, pp 154–158 | Cite as

A note on ℵ-spaces and sn-metrizable spaces

  • Zhaowen Li
  • Qingguo Li
Article
  • 22 Downloads

Abstract

In this paper we give two mapping theorems on ℵ-spaces and sn-metrizable spaces by means of some sequence-covering mappings and mssc-mappings, and get characterizations of quotient (pseudo-open) mssc-images of metric spaces.

Key words and phrases

ℵ-Spaces sn-metrizable spaces strong compact-covering mappings 1-sequence-covering mappings sequence-covering mappings sequentially-quotient mappings mssc-mappings 

2000 Mathematics Subject Classification

Primary 54C10, 54E99 Secondary 54E40, 54E99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Arhangel’skii, Mappings and spaces, Russian Math. Surveys 21, 115 (1966).CrossRefMathSciNetGoogle Scholar
  2. 2.
    Shou Lin, Locally countable collections, locally finite collections and Alexandroff’s problems, Acta Math. Sinca 37, 491 (1994).MATHGoogle Scholar
  3. 3.
    Shou Lin, Generalized metric spaces and mappings, Chinese (Scientific Publ., Beijing, 1995).Google Scholar
  4. 4.
    L. Foged, Characterizations of ℵ-spaces, Pacific J.Math. 110, 59 (1984).MATHMathSciNetGoogle Scholar
  5. 5.
    J. Nagata, General metric spaces I, in Topics in General Topology (North-Holland, Amsterdam, 1989).Google Scholar
  6. 6.
    Shou Lin, A note onMichael-Nagami’s problem, Ann. Math. 17, 9 (1996).MATHGoogle Scholar
  7. 7.
    Shou Lin, On sequence-covering s-mappings, Adv. in Math. 25, 548 (1996).MATHGoogle Scholar
  8. 8.
    Shou Lin, Chuan Liu, and Mumin Dai, Images on locally separable metric spaces, Acta Math. Sinica, New series, 13, 1 (1997).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    G. Gruenhage, E. Michael, and Y. Tanaka, Spaces determined by point-countable covers, Pacific J. Math. 113 (1984).Google Scholar
  10. 10.
    Ying Ge, On sn-metrizable spaces, Acta Math. Sinica 45, 355 (2002).MATHGoogle Scholar
  11. 11.
    Ying Ge, Spaces with countable sn-networks, Comment. Math. Univ. Carolinae 45, 169 (2004).MATHGoogle Scholar
  12. 12.
    S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57, 107 (1965).MATHMathSciNetGoogle Scholar
  13. 13.
    J. Boone and F. Siwiec, Sequentially-quotient mappings, Czech Math. J. 26, 174 (1976).MathSciNetGoogle Scholar
  14. 14.
    Y. Tanaka and Zhaowen Li, Certain covering-maps and k-networks, and related matters, Topology Proc. 27, 317 (2003).MATHMathSciNetGoogle Scholar
  15. 15.
    Zhaowen Li and Shou Lin, On the weak-open images of metric spaces, Czech. Math. J. 54, 393 (2004).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.College of InformationHunan University of CommerceChangsha, HunanP.R. China
  2. 2.College of Mathematics and EconometricsHunan UniversityChangsha, HunanP.R. China

Personalised recommendations