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International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 439-452
http://dx.doi.org/10.1155/S0161171298000611

Probabilistic convergence spaces and generalized metric spaces

Washington State University, Pullman 99164-3113, WA., USA

Received 25 June 1996

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The category PPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom (Δ) and whose morphisms are continuous mappings, is introduced. Categories consisting of generalized metric spaces as objects and contraction mappings as morphisms are embedded as full subcategories of PPRS(Δ). The embeddings yield a description of metric spces and their most natural generalizations entirely in terms of convergence criteria.