When is a Discrete Bounded Subgroup of an LCA Group Necessarily a Topological Direct Summand?
We establish necessary and sufficient conditions for a discrete bounded subgroup of an LCA (locally compact abelian) group to be a topological direct summand. This yields a characterization of splitting LCA groups whose torsion part is discrete.
Loth, P. (2000). When is a discrete bounded subgroup of an LCA group necessarily a topological direct summand? Far East Journal of Mathematical Sciences (FJMS), 2(6), 929-934.