Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

METRIZABILITY AND SUBMETRIZABILITY FOR POINT-OPEN, OPEN-POINT AND BI-POINT-OPEN TOPOLOGIES ON C(X, Y)

  • Received : 2020.12.16
  • Accepted : 2021.12.24
  • Published : 2022.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

Keywords

Acknowledgement

The authors are thankful to referee for valuable suggestions and comments which led to a considerable improvement of the earlier version of this paper.

References

  1. A. Arhangel'skii and M. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, 1, Atlantis Press, Paris, 2008. https://doi.org/10.2991/978-94-91216-35-0
  2. A. V. Arkhangel'skii, Topological function spaces, translated from the Russian by R. A. M. Hoksbergen, Mathematics and its Applications (Soviet Series), 78, Kluwer Academic Publishers Group, Dordrecht, 1992.
  3. A. Jindal, R. A. McCoy, and S. Kundu, The open-point and bi-point-open topologies on C(X), Topology Appl. 187 (2015), 62-74. https://doi.org/10.1016/j.topol.2015.02.004
  4. A. Jindal, R. A. McCoy, and S. Kundu, The open-point and bi-point-open topologies on C(X): submetrizability and cardinal functions, Topology Appl. 196 (2015), part A, 229-240. https://doi.org/10.1016/j.topol.2015.09.042
  5. R. A. McCoy and I. Ntantu, Topological properties of spaces of continuous functions, Lecture Notes in Mathematics, 1315, Springer-Verlag, Berlin, 1988. https://doi.org/10.1007/BFb0098389
  6. A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, reprint of the second edition, Robert E. Krieger Publishing Co., Inc., Melbourne, FL, 1986.