An Investigation Of The Strongness Property For Nearness Frames

Abstract

This study will investigate the strongness property for nearness and nearness partial frames. We initially revisit the concepts of strong and totally strong nearness frame and study their closures under completion. We also explore the properties of totally strong and uniformly completely regular nearness frames, and study the relationship between them. We show that the category of totally strong nearness frames is coreflective in the category of uniformly completely regular nearness frames. This we do by constructing the coreflection. Further, we study nearness in the context of partial frames with particular emphasis to the strong and totally strong properties. We follow [6] in constructing the respective coreflections using the notion of P-Approximations.