On topological rough groups

TL;DR

This paper introduces the concepts of topological rough groups, explores their properties, and constructs related structures such as homomorphisms, actions, and spaces, providing foundational insights into their theoretical framework.

Contribution

It presents a comprehensive introduction to topological rough groups, including new definitions, properties, and constructions like products and homomorphisms, advancing the theoretical understanding of rough algebraic structures.

Findings

Defined topological rough groups and homomorphisms

Constructed the product of topological rough groups with examples

Introduced rough actions, homogeneous spaces, and kernels

Abstract

In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an illustrated example. Then, we define topological rough group homomorphisms and topological rough group homeomorphisms. Finally, we introduce a rough action, a rough homogenous space and a rough kernel.