International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 4, Pages 637-646
doi:10.1155/S0161171297000896

Probablistic convergence spaces and regularity

P. Brock and D. C. Kent

 Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-3113, WA, USA
Received 5 February 1996; Revised 20 May 1996

Abstract

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.