A note on quasi irresolute topological groups

Subject Areas : History and biography

T. Oner ¹ , A. Ozek ²

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

Received: 2016-01-28 Accepted : 2016-04-25 Published : 2016-06-01

Keywords: Semi-open set, semi-closed set, irresolute mapping, semi-homeomorphism, quasi irresolute topological group,

Abstract :

In this study, we investigate the further properties of quasi irresolute topological groupsdefined in [20]. We show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connectedquasi 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 irresolutetopological group $(G,*,\tau)$ is semi-discrete if and only if it has a semi-isolated point.

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