Covering L-locally uniform spaces

Abstract

In this paper, we develop the notion of covering 𝐿 −locally uniform spaces. Interior and closure operators were then introduced to show that every covering 𝐿 −local uniformity induced a regular 𝐿 −topology and vice-versa. Further, we have introduced the notion of weakly uniformly continuous functions in the class of covering 𝐿 −local uniformities and studied some of its basic properties. We then established that the products of 𝐿 −regular topologies are generated by the product covering 𝐿 −locally uniform space. Towards the end of this paper, we have shown that every covering 𝐿 −locally uniform spaces with countable base is pseudo-metrisable.