Advertisement

On separability of the functional space with the open-point and bi-point-open topologies

  • A. V. Osipov
Article
  • 4 Downloads

Abstract

We study the property of separability of functional space C(X) with the open-point and bi-point-open topologies and show that it is consistent with ZFC that there is a set of reals of cardinality \({\mathfrak{c}}\) such that a set C(X) with the open-point topology is not a separable space. We also show in a set model (the iterated perfect set model) that for every set of reals X, C(X) with the bi-point-open topology is a separable space.

Key words and phrases

open-point topology bi-point-open topology separability strongly null set 

Mathematics Subject Classification

54C40 54C35 54D60 54H11 46E10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jindal A., McCoy R.A., Kundu S.: The open-point and bi-point-open topologies on C(X): Submetrizability and cardinal functions. Topology Appl., 196, 229–240 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Jindal A., McCoy R.A., Kundu S.: The open-point and bi-point-open topologies on C(X). Topology Appl., 187, 62–74 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Kazimirz Kuratowski, Topology, Vol. I, Academic Press (New York–London, 1966).Google Scholar
  4. 4.
    Miller A.W.: Mapping a set of reals onto the reals. J. Symbolic Logic, 48, 575–584 (1983)MathSciNetCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsUral Federal UniversityEkaterinburgRussia

Personalised recommendations