Generalized quasi-proximities

This paper studies several kinds of fuzzy quasi-proximities. Firstly, we introduce generalized pointwise S-quasi-proximities and prove that S-FPQPS—the category of generalized pointwise S-quasi-proximity spaces—is isomorphic to TFRNS—the category of topological fuzzy remote neighborhood spaces. Secondly, we introduce generalized S-quasi-proximities and prove that S-FQPS—the category of generalized S-quasi-proximity spaces—is isomorphic to S-FPQPS. Finally, we study generalized quasi-proximities and discuss the relationships between this kind of quasi-proximities and generalized pointwise quasi-uniformities.