Equations in \(\beta G\) and the resolvability of abelian groups (Q1582824)

In this paper, the author continues his study of resolvability in Abelian groups with some weak continuity assumptions. A space is called resolvable (resp. \(\omega\)-resolvable) if it can be decomposed into two (countably many) dense subsets. A typical result says: let \(G\) be an Abelian group with a nondiscrete topology such that all translations are continuous. Assume further that the equation \(2g=0\) has only finitely many solutions in \(G\). Then \(G\) is resolvable. Some analogous but stronger finiteness assumptions yield \(\omega\)-resolvability. Proofs are replaced by the hint that some methods applied by the author in earlier papers carry over to the present situation.