Öner, T.; Özek, A. A note on quasi irresolute topological groups. (English) Zbl 1424.54073 J. Linear Topol. Algebra 5, No. 1, 41-46 (2016). Summary: In this study, we investigate the further properties of quasi irresolute topological groups defined in [T. Öner et al., J. Adv. Stud. Topol. 4, No. 3, 23–28 (2013; Zbl 1338.54144)]. 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 \((G,\ast,\tau )\), 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 \((G,\ast,\tau)\) is semi-discrete if and only if it has a semi-isolated point. Cited in 2 Documents MSC: 54H11 Topological groups (topological aspects) 22A05 Structure of general topological groups 54C08 Weak and generalized continuity 54H99 Connections of general topology with other structures, applications Keywords:semi-open set; semi-closed set; irresolute mapping; semi-homeomorphism; quasi irresolute topological group Citations:Zbl 1338.54144 PDFBibTeX XMLCite \textit{T. Öner} and \textit{A. Özek}, J. Linear Topol. Algebra 5, No. 1, 41--46 (2016; Zbl 1424.54073) Full Text: Link