Topological groups in which each nowhere dense subset is closed (Q1282527)

It is proved under the combinatorial principle \(p=\mathfrak c\) (which is also called Booth lemma) that any nondiscrete metrizable group topology on an Abelian group can be strengthened to a nondiscrete group topology such that each nowhere dense subset is closed. Recall that the Martin's axiom (and therefore also the continuum hypothesis) implies the validity of the combinatorial principle \(p=\mathfrak c\).