Resolvability of topological groups

Abstract

A topological group is called resolvable (ω-resolvable) if it can be partitioned into two (into ω) dense subsets and absolutely resolvable (absolutely ω-resolvable) if it can be partitioned into two (into ω) subsets dense in every nondiscrete group topology. These notions have been intensively studied over the past 20 years. In this dissertation some major results in the field are presented. In particular, it is shown that (a) every countable nondiscrete topological group containing no open Boolean subgroup is ω-resolvable, and (b) every infinite Abelian group containing no infinite Boolean subgroup is absolutely ω-resolvable.