Covering Fuzzy Uniform Spaces

Topological, proximal and uniform structures on the fuzzy spaces are defined using different set of axioms and basic terms. There are various equivalent definitions in literature even for each of these structures. Since the late seventies and early eighties uniformity in fuzzy topology was studied by three authors. B. Hutton[5] , U. H?hle[3,4], and R. Lowen[8]. The approaches of U. H?hle and R. Lowen underpinned by power sets of the form I X ×X or T and B. Hutton approach is based on exponential power sets of the form ? ? T . T X X X ×X Recently, a different approach to fuzzy uniformities, in terms of T -covers was introduced which seems the most natural one. In this paper we investigate some properties of T - valued uniformities and we will show that a functor between Hutton uniformities and T - valued uniformities.