Discrete Topological Space as a Space in Finite Geometry with Variables in Integer Modulo m

Abstract

This paper explores the construction of discrete topological spaces on non-near-linear finite geometries, where points and lines are defined over the ring of integers modulo m. By introducing a partial order among subgeometries, we demonstrate how such structures satisfy the axioms of topology and provide illustrative examples for specific cases such as finite geometry  The geometry under discourse together with the collection of its subsets called subgeometry yields a discrete topological space with its subgeometries as topology.