Continuity of some mappings on a group via semi-regular topology
محورهای موضوعی : Topological groups, Lie groups
1 - Department of Mathematics, University of Jammu, Jammu-180006, Jammu & Kashmir, India
2 - Department of Mathematics and Statistics, Faculty of Sciences, P.O. 888, Taif University, Saudi Arabia
کلید واژه: regularly open sets, semi-regular topology, virtually topological groups, super topological groups, $delta-$open sets,
چکیده مقاله :
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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