Dense subgroups of paratopological groups
A paratopological group (semitopological group) is a group with a topology such that the multiplication operation is jointly (separately) continuous. In this paper, the author focus on some properties in semitopological groups which are preserved or determined by dense subgroups. Many propositions for this kind of properties are given. For example, (1) letting \(H\) be a dense subgroup of a \(T_3\) semitopological group \(G\), if \(H\) is a paratopological group, then \(G\) is a paratopological group as well; (2) a semitopological group \(G\) is a topological group iff \(G\) is \(T_3\) and it contains a dense topological subgroup. Many counterexamples for this kind of properties are also presented in this paper. In the end, the author answers a problem posed by \textit{M. Tkachenko} [Topology Appl. 179, 200--214 (2015; Zbl 1305.54024)] in the negative.
scientific article; zbMATH DE number 6509447