Continuity of some mappings on a group via semi-regular topology

Journal of Linear and Topological Algebra

دوره 10، شماره 03، آذر 2021، صفحه 179-185   

نوع مقاله: Research Paper

نویسندگان

M. Ram^{* 1}؛ S. K. Elagan²

¹Department of Mathematics, University of Jammu, Jammu-180006, Jammu & Kashmir, India

²Department of Mathematics and Statistics, Faculty of Sciences, P.O. 888, Taif University, Saudi Arabia

چکیده

‎For a given topological space $(X‎, ‎~\Im)$,‎ ‎there is a coarser topology on $X$ which is called the semi-regular topology on $X$ (generated by regularly open subsets) and it is denoted by $\Im^{\delta}$‎. ‎In this paper‎, ‎we study the continuity of the group operation and the inversion mapping ($\varsigma\longmapsto\varsigma^{-1}$) as regards the semi-regular topology $\Im^{\delta}$ (not necessarily with the given topology)‎. ‎Then we study the said mappings with the blend of the given topology $\Im$ and the semi-regular topology $\Im^{\delta}$‎. ‎In the twilight of this note‎, ‎we pose some questions which are noteworthy‎.

کلیدواژه‌ها

$delta-$open sets‎؛ ‎regularly open sets‎؛ ‎semi-regular topology‎؛ ‎virtually topological groups‎؛ ‎super topological groups

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