Acta Mathematica Hungarica

, Volume 146, Issue 2, pp 376–390 | Cite as

Probabilistic uniform convergence spaces redefined

Article
First Online:
Received:
Revised:
Accepted:

Abstract

We develop a theory of probabilistic uniform convergence spaces based on Tardiff’s neighbourhood systems for probabilistic metric spaces. We show that the resulting category is topological and Cartesian closed. A subcategory is identified that is isomorphic to the category of probabilistic metric spaces.

Key words and phrases

probabilistic metric space probabilistic uniform convergence space probabilistic uniform space distance distribution function 

Mathematics Subject Classification

54E70 54E15 54A20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Adámek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, Wiley (New York, 1989).Google Scholar
  2. 2.
    Cook C.H., Fischer H.R.: Uniform convergence structures. Math. Ann. 173, 290–306 (1967)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Florescu L.C.: Probabilistic convergence structures. Aequationes Math. 38, 123–145 (1989)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Fritsche R.: Topologies for probabilistic metric spaces. Fund. Math. 72, 7–16 (1971)MathSciNetMATHGoogle Scholar
  5. 5.
    G. Jäger, A convergence theory for probabilistic metric spaces, Quaestiones Math., to appear.Google Scholar
  6. 6.
    Nusser H.: A generalization of probabilistic uniform spaces. Appl. Categ. Structures 10, 81–98 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    G. Preuss, Foundations of Topology. An Approach to Convenient Topology, Kluwer Academic Publishers (Dordrecht, 2002).Google Scholar
  8. 8.
    Saminger-Platz S., Sempi C.: A primer on triangle functions I. Aequationes Math. 76, 201–240 (2008)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Saminger-Platz S., Sempi C.: A primer on triangle functions II. Aequationes Math. 80, 239–261 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland (New York, 1983).Google Scholar
  11. 11.
    Sibley D.A.: A metric for weak convergence of distribution functions. Rocky Mountain J. Math. 1, 427–430 (1971)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Tardiff R.M.: Topologies for probabilistic metric spaces. Pacific J. Math. 65, 233–251 (1976)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    O.Wyler, Filter space monads, regularity, completions, in: TOPO 1972 General Topology and its Applications, Lecture Notes in Mathematics, Vol. 378, Springer (Berlin, Heidelberg, New York, 1974), 591–637.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Department of MathematicsKing Saud UniversityRiyadhSaudi Arabia
  2. 2.School of Mechanical EngineeringUniversity of Applied SciencesStralsundGermany

Personalised recommendations