On $G$-sequential connectedness

TL;DR

This paper explores the properties of $G$-sequential connectedness in Hausdorff topological groups, extending the concept and establishing new theorems about its characteristics.

Contribution

It advances the understanding of $G$-sequential connectedness by investigating its properties and proving new theorems in the context of topological groups.

Findings

Characterization of $G$-sequential connectedness

Theorems on $G$-sequential connectedness properties

Extension of $G$-sequential connectedness concepts

Abstract

Recently, Cakalli has introduced a concept of $G$-sequential connectedness in the sense that a non-empty subset $A$ of a Hausdorff topological group $X$ is $G$-sequentially connected if there are no non-empty, disjoint $G$-sequentially closed subsets $U$ and $V$ meeting $A$ such that $A\subseteq U\bigcup V$. In this paper we investigate further properties of $G$-sequential connectedness and prove some interesting theorems.