Subgroups of paratopological groups and feebly compact groups (Q2922060)

The authors mainly prove the following results: (1) If all countable subgroups of a semitopological group \(G\) are precompact, then \(G\) is also precompact and the closure of an arbitrary subgroup of \(G\) is again a subgroup. (2) The authors give a general method of refining the topology of a given paratopological group \(G\) such that the group \(G\) with the finer topology, say \(\sigma\), is again a paratopological group containing a subgroup whose closure in (\(G, \sigma\)) is not a subgroup. (3) Each feebly compact paratopological group \(H\) is perfectly \(\kappa\)-normal; (4) Each \(G_\delta\)-dense subspace of a feebly compact \(H\) is feebly compact.