On Generalized Quasi-uniformity and Generalized Quasi-uniformizable supratopological spaces

Abstract

In this paper, introducing generalized quasi uniformity (in short, \(g\)-quasi uniformity) and \(g\)-quasi uniformly continuous maps, it has been shown that every supratopology is achievable from a \(g\)-quasi uniformity; moreover, a \(g\)-continuous map between a pair of supratopological spaces is indeed the induced map obtained from the \(g\)-quasi uniformly continuous map between the corresponding \(g\)-quasi uniform spaces. These results establish a functorial correspondence between the respective categories. Descriptions of \(g\)-neighbourhood system, \(g\)-interior operator and subspaces of GTS alongwith a characterization of \(\mu\)-\(T_1\)-ness of a GTS in terms of \(g\)-quasi uniformity are established. Further, introducing \(g\)-quasi uniform isomorphism in a natural way, a couple of \(g\)-quasi uniform properties are also discussed.