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

Subject Areas : Topological groups, Lie groups

M.  Ram ¹ (Department of Mathematics, University of Jammu, Jammu-180006, Jammu & Kashmir, India)
S. K.  Elagan ² (Department of Mathematics and Statistics, Faculty of Sciences, P.O. 888, Taif University, Saudi Arabia)

Received: 2020-03-05 Accepted : 2021-07-20 Published : 2021-09-01

Keywords: ‎regularly open sets‎, ‎semi-regular topology‎, ‎virtually topological groups‎, ‎super topological groups, $delta-$open sets‎,

Abstract :

‎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.

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