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A NOTE ON WEAKLY FIRST COUNTABLE SPACES

  • Hon, Woo-Chorl (Department of Mathematics Education Pusan National University)
  • Published : 2002.07.01

Abstract

We prove that the star operator and the sequential closure operator on a weakly first countable space are the same and show that the Frechetness is a sufficient condition for a weakly first countable space to be first countable.

Keywords

star operator;sequential closure operator;Frechet;first countable;weakly first countable;symmetrizable;semi-metrizable

References

  1. Springer-Verlage EMS v.17 General Topology Ⅰ A. V. Arhangel'skii;L. S. Pontryagin(Eds.)
  2. Annals of the New York Academy of Sciences v.278 k-structures and topology R. E. Hodel
  3. Commun. Korean Math. Soc. v.13 no.2 Some properties of the sequential closure operator on a generalized topological space W. C. Hong
  4. Russian Math. Surveys v.21 Mappings and spaces A. V. Arhangel'skii
  5. Pacific J. of Math. v.52 no.1 On defining a space by a weak base F. Siwiec
  6. HandBook of Set-Theoretic Topology Generalized metric spaces G. Gruenhage

Cited by

  1. STAR OPERATORS ON sn-NETWORKS vol.27, pp.3, 2012, https://doi.org/10.4134/CKMS.2012.27.3.621
  2. The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces vol.69, pp.1, 2019, https://doi.org/10.1515/ms-2017-0213