A note on quasi irresolute topological groups

Abstract

In this study, we investigate the further properties of quasi irresolute topological groups defi ned in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then $G$ is generated by $V$. Moreover it is proven that a subgroup $H$ of a quasi irresolute topological group $(G,*,tau)$ is semi-discrete if and only if it has a semi-isolated point.