Convenient categories for topologists

Abstract

The category Top of R-topological space is nicely embedded in Grill and Conv, two cartesian closed topological categories of nearness spaces Grill is a quasi-topos which| although constructible .fromTop : in a natural way, contains the contiguity and proximity spaces as bireflective subcategories* Conv, bicreflective in Grill, is isomorphic to the category of symmetric convergence spaces .