A note on the category of quasi-proximity spaces

Abstract

We characterize the separation properties T0 and T1 at a point p in the category of quasi-proximity spaces. Moreover, the (strongly) closed and (strongly) open subobjects of an object, and each of the various notions of connected and compact objects are characterized in this topological category.

A Note on Quotient Reflective Subcategories of O-REL

“…Classical separation axioms at some point p (locally) were generalized and have been inspected in [14], where the purpose was to describe the notion of strongly closed sets (resp., closed) in arbitrary set based topological categories [19]. Moreover, the notions of compactness [20], Hausdorffness [14], regular and normal objects [21], perfectness [20], and soberness [22] have been generalized by using the closed and strongly closed sets in some well-defined topological categories over sets [20,[23][24][25][26]. Furthermore, the notion of closedness is suitable for the formation of closure operators [27] in several well-known topological categories [28][29][30].…”