Probablistic convergence spaces and regularity - P. Brock; D. C. Kent (International Journal of Mathematics and Mathematical Sciences)
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.