L-Fuzzy Topogenous Spaces and L-fuzzy Quasi-Uniform Spaces

摘要

We introduce the concept of L-fuzzy topogenous structures in the framework of L-fuzzy topologies and L-fuzzy quasi-proximities. Some fundamental properties of them are established. We study a natural relationship between L-fuzzy topogenous structures and L-fuzzy quasi-uniformities. The family Π(η) of all L-fuzzy quasi-uniformities U compatible with an L-fuzzy topogenous structure η on X is never empty and it contains an L-fuzzy quasi-uniformity U_η which is the coarsest member of Π(η).