On local function, an algebraic approach

TL;DR

This paper introduces an algebraic framework for topological structures in groups using ideals and anti-ideals, emphasizing how homomorphic images transform these structures.

Contribution

It presents a novel algebraic approach to defining and manipulating topological group structures through ideals and anti-ideals.

Findings

Established a new topological structure in groups using ideals.

Showed how homomorphic images alter these topological structures.

Connected algebraic ideals with topological concepts in groups.

Abstract

The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the remarkable role to change the topological structure from one system to another system.