International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 439-452
doi:10.1155/S0161171298000611
Probabilistic convergence spaces and generalized metric spaces
Washington State University, Pullman 99164-3113, WA., USA
Received 25 June 1996
Copyright © 1998 Paul Brock. 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.