Topogenous and Nearness Structures on Categories

Abstract

We introduce topogenous orders on a general category and demonstrate that they are equivalent to neighbourhood operators and subsume both closure and interior operators. By looking at the basic properties of so-called strict morphisms relative to a topogenous order the ease of working with their axioms and the concurrent generalisation of both interior and closure is evident. In closing we consider Herrlich’s concept of nearness in a category and how it interacts with topogenous orders and syntopogenous structures.