Compact-Like Totally Dense Subgroups of Compact Groups
Compact-Like Totally Dense Subgroups of Compact Groups
A subgroup H of a topological group G is (weakly) totally dense in G if for each closed (normal) subgroup N of G the set H n N is dense in A'.We show that no compact (or more generally, to-bounded) group contains a proper, totally dense, countably compact subgroup.This yields …