In this paper we study
semi-metric and developable spaces via generalized proximities and uniformities. We
find sufficient conditions for a compatible semi-metric d on a space X to induce a
Lodato proximity and also study the effects on a space X when d satisfies various
weaker forms of continuity. We present two new characterizations of developable
spaces, one of which reads: A T1-space is developable if and only if it has a
compatible upper semi-continuous semimetric. We give improved versions of two
known metrization theorems. Finally, we generalize the concepts: T1-map, uniform
map, completely uniform map, pseudo-open map, etc., to apply to proximity spaces
and improve some of the known results: for example, an open uniform image of a
developable space is developable.
