Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Science Mugla Sitk Kocman University, Mugla 48000, Turkey

2 Department of Mathematics, Graduate School of Natural and Applied Sciences Mugla Sitki Kocman University, Mugla 48000, Turkey

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.

Keywords

Main Subjects

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