Advertisement

manuscripta mathematica

, Volume 38, Issue 3, pp 265–287 | Cite as

Compactness notions in fuzzy neighborhood spaces

  • Robert Lowen
Article

Abstract

In the class of fuzzy neighborhood spaces we demonstrate which implications hold and give counterexamples to the implications which do not hold between the notions of compactness, α-compactness, strong compactness and ultra compactness.

Keywords

Number Theory Algebraic Geometry Topological Group Strong Compactness Neighborhood Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    CHANG C.L.: Fuzzy topological spaces, J. Math. Anal. Appl.24, 182–190 (1968)Google Scholar
  2. 2.
    GANTNER T.E., STEINLAGE R.C. and WARREN R.H.: Compactness in fuzzy topological spaces, J. Math. Anal. Appl.62, 547–562 (1978)Google Scholar
  3. 3.
    GOGUEN J.A.: The fuzzy Tychonoff theorem, J. Math. Anal. Appl.43, 734–742 (1973)Google Scholar
  4. 4.
    HOHLE U.: Probabilistische Topologien, Manuscripta Mathematica26, 223–245 (1978)Google Scholar
  5. 5.
    —: Probabilistisch kompakte L-unscharfe Mengen, Manuscripta Mathematica26, 331–347 (1979)Google Scholar
  6. 6.
    LOWEN R.: Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl.56, 621–633 (1976)Google Scholar
  7. 7.
    —: A comparison of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl.64, 446–454 (1978)Google Scholar
  8. 8.
    —: Convergence in fuzzy topological spaces, General Topology and its Applications10, 147–160 (1979)Google Scholar
  9. 9.
    —: Fuzzy uniform spaces, J. Math. Anal. Appl.82, 370–385 (1981)Google Scholar
  10. 10.
    —: Fuzzy neighborhood spaces, J. Fuzzy Sets and Systems7, 165–189 (1982)Google Scholar
  11. 11.
    WONG C.K.: Covering properties of fuzzy topological spaces, J. Math. Anal. Appl.43, 697–704 (1973)Google Scholar
  12. 12.
    ZADEH L.A.: Fuzzy Sets, Inf. Contr.8, 338–353 (1965)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Robert Lowen
    • 1
  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselBelgium

Personalised recommendations