A note on quasi irresolute topological groups

Journal of Linear and Topological Algebra

مقاله 4، دوره 05، شماره 01، اردیبهشت 2016، صفحه 41-46   

نوع مقاله: Research Paper

نویسندگان

T. Oner^{* 1}؛ A. Ozek²

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

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

چکیده

In this study, we investigate the further properties of quasi irresolute topological groups defined 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.

کلیدواژه‌ها

Semi-open set؛ semi-closed set؛ irresolute mapping؛ semi-homeomorphism؛ quasi irresolute topological group

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