t -prefilter theory

Abstract In the first part of this paper, the notion of t -prefilter is introduced and studied, as are the applications λ t and ω t , their properties and relations between them. We characterize the minimal prime t -prefilters finer than a given t -prefilter, by using ultrafilters on X : and we give equivalents conditions of the t -maximality. In the second part, we define t -convergence, and we obtain a characterization of t -compactness (Gantner-Steinlage) by means of the maximal t -prefilters. Finally, some applications of these concepts, related to the continuity, separation axioms and fuzzy compactness are studied.