Characterization of TL-uniform spaces by coverings

Abstract

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) [4] . 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.