On partitions of groups into dense subsets
A group is called absolutely resolvable (absolutely \(\omega\)-resolvable) if it can be partitioned into two (into \(\omega)\) subsets dense in any nondiscrete group topology. The author proves the basic theorems: (1) Every countable \(\omega\)-irresolvable topological group contains an open Boolean subgroup. (2) Every countable group with finitely many elements of order 2, that can be embedded in a compact topological group, is absolutely \(\omega\)-resolvable.
scientific article; zbMATH DE number 1891215