Fuzzy TL-uniform spaces - Khaled A. Hashem; Nehad N. Morsi (International Journal of Mathematics and Mathematical Sciences)
The main purpose of this paper is to introduce a new structure that is a fuzzy TL-uniform space. We show that our structure generates a fuzzy topological space, precisely, a fuzzy T-locality space. Also, we deduce the concept of level uniformities of a fuzzy TL-uniformity. We connect the category of fuzzy TL-uniform spaces with the category of uniform spaces. We establish a necessary and sufficient condition, under which a fuzzy TL-uniformity is probabilistic pseudometrizable. Finally, we define a functor from the category of fuzzy TL-uniform spaces into the category of fuzzy T-locality spaces and we show that it preserves optimal lifts.