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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 4, Pages 637-646

Probablistic convergence spaces and regularity

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USA

Received 5 February 1996; Revised 20 May 1996

Copyright © 1997 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.


The usual definition of regularity for convergence spaces can be characterized by a diagonal axiom R due to Cook and Fischer. The generalization of R to the realm of probabilistic convergence spaces depends on a t-norm T, and the resulting axiom RT defines “T-regularity”, which is the primary focus of this paper. We give several characterizations of T-regularity, both in general and for specific choices of T, and investigate some of its basic properties.