Topological Space: A Space in Finite Dimensional Euclidean Plane with Variables in "Z(q)"

Abstract

This work centres on a finite dimensional Euclidean geometry with variables in called near-linear finite geometry. In it, we investigate points and lines in the geometry. A set of points joined together forms lines in the geometry and a presence of trivial divisors yields a set together with the collection of only two subsets, that is, the whole set itself and integer one as members with subgeometries as induced topology where the only open set is the universal set and an empty set. We prove that the Euclidean plane for prime forms an indiscrete topological space whose open sets are trivial subgeometries, and