UNIFORMITIES ON COMPLETELY DISTRIBUTIVE LATTICES

In order to study fuzzy topology and general topology in view of topological lattice, many researches have been carried out. Because of the lack of reverse order involution, there are some fundamental works, such as the theory of uniformity and metrization to be considered. In this note, we introduce the notion of uniformity on completely distributive lattice in terms of cover systems, and show that it is a good extension, we obtain some properties and prove that the equivalence of complete regularity and uniformizability on completely distributive lattices.