TOPOLOGICAL RINGS THROUGH THE LENS OF h-OPEN SETS

Abstract

This paper centers around the introduction of two novel concepts: h-topological ring and h-irresolute topological ring defined through the lens of h-open sets. A h-topological ring may not necessarily qualify as a topological ring. We also produced several examples of h-topological rings within infinite topological spaces characterized by co-countable and co-finite topology. Additionally, several essential properties of h-irresolute topological rings and h-topological rings are analyzed. This paper examines the translation of open and closed sets in an h-topological ring and an h-irresolute topological ring via an invertible element. A subring of a h-topological ring (or h-irresolute topological ring) exhibits closure(h-closure), which is also an h-topological ring (or h-irresolute topological ring).