Characterizing Subgroups of Compact Abelian Groups
  We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter. 
Dikran Dikranjan and Kenneth Kunen