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A note on quasi irresolute topological groups. (English) Zbl 1424.54073

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.

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

Citations:

Zbl 1338.54144
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