International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 14, Article ID 25094, 24 pages
doi:10.1155/IJMMS/2006/25094
Fuzzy TL-uniform spaces
Khaled A. Hashem1
and Nehad N. Morsi2
1Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
2Basic \& Applied Science Department, Arab Academy for Sciences \& Technology and Maritime Transport, P.O. Box 2033, Al-Horraya, Heliopolis, Cairo, Egypt
Abstract
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.