Hyperspace of a fuzzy quasi-uniform space

Document Type : Research Paper


1,2Instituto Universitario de Matem´atica Pura y Aplicada, Universitat Polit`ecnica de Val`encia, Camino de Vera s/n, 46022 Valencia, Spain


The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi \cite{Morsi94} and Georgescu \cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the categories of those objects. We will demonstrate the commutativity of these endofunctors with Lowen and Katsaras' functors. Furthermore, we will prove the compatibility of our construction with the Hausdorff fuzzy quasi-pseudometric introduced in \cite{RLRoSA10}.