On Cartesian Powers of a Rational Group.
We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups for which is regular is given.
It is proved that every uncountable -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.