International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 25094, 24 pages
Fuzzy -uniform spaces
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
Received 12 September 2005; Revised 12 April 2006; Accepted 25 April 2006
Copyright © 2006 Khaled A. Hashem and Nehad N. Morsi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The main purpose of this paper is to introduce a new structure
that is a fuzzy -uniform space. We show that our structure
generates a fuzzy topological space, precisely, a fuzzy
-locality space. Also, we deduce the concept of level
uniformities of a fuzzy -uniformity. We connect the category
of fuzzy -uniform spaces with the category of uniform spaces.
We establish a necessary and sufficient condition, under which a
fuzzy -uniformity is probabilistic pseudometrizable. Finally,
we define a functor from the category of fuzzy -uniform spaces
into the category of fuzzy -locality spaces and we show that it
preserves optimal lifts.