Advertisement

A zero-dimensional not strongly zero-dimensional X with Lindelöf Open image in new window

  • Oleg OkunevEmail author
  • Alfredo Sánchez Jiménez
Research Article
  • 8 Downloads

Abstract

We prove, modifying Dowker’s example, that there exists a normal space X such that Open image in new window is Lindelöf, X is zero-dimensional and is not strongly zero-dimensional.

Keywords

Topology of pointwise convergence Lindelöf spaces Zero-dimensional spaces 

Mathematics Subject Classification

54C35 54D20 54G20 

Notes

Acknowledgements

The authors thank the Referees for careful examination of the article and indispensably useful comments.

References

  1. 1.
    Alster, K., Pol, R.: On function spaces of compact subspaces of \(\Sigma \)-products of the real line. Fund. Math. 107(2), 135–143 (1980)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arkhangel’skiĭ, A.V.: Topological Function Spaces. Mathematics and its Applications (Soviet Series), vol. 78. Kluwer, Dordrecht (1992)Google Scholar
  3. 3.
    Engelking, R.: General Topology. Sigma Series in Pure Mathematics, vol. 6. Helderman, Berlin (1989)zbMATHGoogle Scholar
  4. 4.
    Okunev, O.: The Lindelöf number of \(C_{\!p}(X)\times C_{\!p}(X)\) for strongly zero-dimensional \(X\). Cent. Eur. J. Math. 9(5), 978–983 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Okunev, O., Tamano, K.: Lindelöf powers and products of function spaces. Proc. Amer. Math. Soc. 124(9), 2905–2916 (1996)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Benemérita Universidad Autónoma de PueblaPueblaMexico

Personalised recommendations