Completion of probabilistic uniform limit spaces

Abstract

In this article completions of special
probabilistic semiuniform convergence spaces are considered. It turns out that
every probabilitic Cauchy space under a given t-norm T (triangular
norm) has a completion which, in the special case of probabilistic Cauchy
spaces with reference to T = min, coincides
with the Kent-Richardson completion for probabilistic Cauchy spaces. Moreover,
a completion of probabilistic uniform limit spaces T = min
is given which in case of constant probabilistic uniform limit spaces coincides
with the Wyler completion.


Mathematics Subject
Classification (2000): 54A20, 54E15, 54D35



Quaestiones Mathematicae 25 (2002), 125-140