Completeness of Hutton [۰,۱]-quasi-uniformities induced by a crisp uniformity

In \cite{Kats۸۴}, Katsaras introduced a method for constructing a Hu\-tton [۰,۱]-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity.  Moreover, we also show that Katsaras' construction allows to develop a theory of completion of a Hu\-tton [۰,۱]-quasi-uniform space obtained from a uniform space.

Keywords:

uniformity , fuzzy uniform structure , Hutton [۰ , ۱]-quasi-uniformity , completeness