Completeness of Hutton $[0,1]$-quasi-uniformities induced by a crisp uniformity

Document Type : Research Paper


1 Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

2 IInstitut Universitari de Matematiques i Aplicacions de Castello (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castello, Spain


In \cite{Kats84}, Katsaras introduced a method for constructing a Hu\-tton $[0,1]$-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 [0,1]-quasi-uniform space obtained from a uniform space.