On some results in fuzzy metric spaces
Fuzzy Sets and Systems
On some results of analysis for fuzzy metric spaces
Fuzzy Sets and Systems
Some properites of fuzzy metric spaces
Fuzzy Sets and Systems
Completeness of Hutton [0,1]-quasi-uniform spaces
Fuzzy Sets and Systems
Uniform environments as a general framework for metrics and uniformities
Fuzzy Sets and Systems
Fuzzy uniform structures and continuous t-norms
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A representation theorem for fuzzy pseudometrics
Fuzzy Sets and Systems
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It is well known that given a probabilistic metric space (Menger space) with continuous t-norm T there is a Hausdorff topology associated. This association factorizes through strong uniformities (or (@e,@l)-uniformities). Similarly, any fuzzy metric space (X,M,*) can be endowed with a Hausdorff topology @t"M (in the case of fuzzy quasi-metric spaces, a T"1 topology), and again this association factorizes through (quasi-)uniform spaces. In this paper we associate to each fuzzy (quasi-)metric space a Hutton [0,1]-quasi-uniformity U"M. This allows us to give a factorization of the previous association via Hutton [0,1]-quasi-uniformities. It is also proved that the topology @t"M is exactly the image under Lowen's functor @i of the [0,1]-topology induced by U"M. As a consequence, we get a class of Hutton [0,1]-quasi-uniformities which are probabilistic metrizable.