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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Adámek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, Wiley (New York, 1989).
Cook C.H., Fischer H.R.: Uniform convergence structures. Math. Ann. 173, 290–306 (1967)
Florescu L.C.: Probabilistic convergence structures. Aequationes Math. 38, 123–145 (1989)
Fritsche R.: Topologies for probabilistic metric spaces. Fund. Math. 72, 7–16 (1971)
G. Jäger, A convergence theory for probabilistic metric spaces, Quaestiones Math., to appear.
Nusser H.: A generalization of probabilistic uniform spaces. Appl. Categ. Structures 10, 81–98 (2002)
G. Preuss, Foundations of Topology. An Approach to Convenient Topology, Kluwer Academic Publishers (Dordrecht, 2002).
Saminger-Platz S., Sempi C.: A primer on triangle functions I. Aequationes Math. 76, 201–240 (2008)
Saminger-Platz S., Sempi C.: A primer on triangle functions II. Aequationes Math. 80, 239–261 (2010)
B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland (New York, 1983).
Sibley D.A.: A metric for weak convergence of distribution functions. Rocky Mountain J. Math. 1, 427–430 (1971)
Tardiff R.M.: Topologies for probabilistic metric spaces. Pacific J. Math. 65, 233–251 (1976)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ahsanullah, T.M.G., Jäger, G. Probabilistic uniform convergence spaces redefined. Acta Math. Hungar. 146, 376–390 (2015). https://doi.org/10.1007/s10474-015-0525-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-015-0525-6
Key words and phrases
- probabilistic metric space
- probabilistic uniform convergence space
- probabilistic uniform space
- distance distribution function