Skip to main content
SpringerLink
Log in

Finite Quasi-Uniform Extensions. I

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Finite extensions of quasi-uniformities for prescribed topologies are examined. We present a necessary and sufficient condition for the existence of such an extension. We investigate the set of all compatible extensions and derive that this is a sup-distributive lattice. Then we examine the cardinalities and the lattice theoretic properties of these sets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. H. Bing, Extending a metric, Duke Math. J. 14 (1947), 511–519.

    Google Scholar 

  2. Á. Császár, Regular extensions of quasi-uniformities, Studia Sci. Math. Hungar. 14 (1979), 15–26.

    Google Scholar 

  3. Á. Császár, Extensions of quasi-uniformities, Acta Math. Acad. Sci. Hungar. 37 (1981), 121–145.

    Google Scholar 

  4. Á. Császár, Extensions of closure and proximity spaces, Acta Math. Hungar. 55 (1990), 285–300.

    Google Scholar 

  5. J. Deák, Notes on extensions of quasi-uniformities for prescribed topologies, Studia Sci. Math. Hungar. 25 (1990), 231–234.

    Google Scholar 

  6. J. Deák, Extensions of quasi-uniformities for prescribed bitopologies I-II, Studia Sci. Math. Hungar. 25 (1990), 45–91.

    Google Scholar 

  7. J. Deák, Quasi-uniform extensions for finer topologies, Studia Sci. Math. Hungar. 25 (1990), 97–105.

    Google Scholar 

  8. J. Deák, Uniform and proximal extensions with cardinality limitations, Studia Sci. Math. Hungar. 25 (1990), 343–352.

    Google Scholar 

  9. J. Deák, Extending a quasi-metric, Studia Sci. Math. Hungar. 28 (1993), 105–113.

    Google Scholar 

  10. J. Deák, Survey of compatible extensions, in Topology Theory and Applications II, Colloq. Math. Soc. J. Bolyai 55 (1993), 127–175.

  11. P. Fletcher and W. F. Lindgren, Quasi-uniform Spaces Lecture Notes in Pure Appl. Math. 77.

  12. H. J. Kowalsky, Topologische Räume Birkhäuser (Basel, 1961).

    Google Scholar 

  13. H.-P. A. Künzi and N. Ferrario, Bicompleteness of the fine quasi-uniformity, Math. Proc. Camb. Phil. Soc. 109 (1991), 167–186.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mézeskalács Tér 2.V.11, Budapest, 1155, Hungary

    A. Losonczi

Authors
  1. A. Losonczi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Losonczi, A. Finite Quasi-Uniform Extensions. I. Acta Mathematica Hungarica 79, 85–116 (1998). https://doi.org/10.1023/A:1006509822240

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006509822240

Keywords

Search

Navigation