Characterization of TL-uniform spaces by coverings

In this paper we introduce the concepts of fuzzy TL-uniform spaces by means of coverings,
where T stands for any continuous triangular norm. We show that the structure of covering
TL-uniform spaces are isomorphic to fuzzy TL-uniform spaces as defined by Hashem and Morsi
(2006) [5]. In particular, we study the continuity of functions between covering TL-uniform spaces,
the I-topological space associated with a covering TL-uniform space. Also, we define the notions of level covering uniformities for a covering TL-uniformity. Moreover, we deduce a number of functors between categories of covering TL-uniform spaces, fuzzy TL-uniform spaces, covering uniform spaces and uniform spaces.