On initial and final fuzzy uniform structures

Abstract

This paper is devoted to study the initial and final fuzzy uniform structures of the fuzzy uniform structure defined by the author and others in 1998. In this paper, we show that all initial and final lifts in the category FUN of these fuzzy uniform spaces and hence the initial and final fuzzy uniform structures exist. We introduce a characterization for the initial fuzzy uniform structures and as a special initial fuzzy uniform spaces the subspaces and product spaces of these fuzzy uniform spaces can be also characterized. We also show that the fuzzy topology (global homogeneous fuzzy neighborhood structure) associated to the initial fuzzy uniform structure of a family of fuzzy uniform structures coincides with the initial fuzzy topology (initial global homogeneous fuzzy neighborhood structure) of the family of fuzzy topologies (global homogeneous fuzzy neighborhood structures) associated to these fuzzy uniform structures.