-categories
We introduce the structure of a nearness on a -frame and construct the coreflection of the category of nearness -frames to the category of compact regular -frames. This description of the Samuel compactification of a nearness -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform -frames in [11]. We also construct the uniform coreflection of a nearness -frame, that is, the coreflection of the category of to the category...
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...