If G is a topological group, then we say that a subset S of G \{1G} is suitable if (a) it is relatively discrete, (b) its closure in G is contained in S \cup {1G}, and (c) the group generated in G by S is dense in G. In this paper we study to what extent the property of having a suitable set is productive, and viceversa. Thus we find some classes of groups that have suitable sets and examples of groups that do not, the latter achieved sometimes with the additional set theoretic assumption MA(\sigma-centered). As for the former, we prove that locally compact Abelian groups equipped with their Bohr topology always have a suitable set.
Mathematics Subject Classification: 03E50, 22A05, 22A10, 22B05, 54D30, 54D65, 54H11
Keywords: Suitable set, totally bounded group, countably compact space, sequentially compact space, Martin's axiom (\sigma-centered), continuum hypothesis, free (Abelian) group, transversal set, Bohr compactification, Bohr topology
Date received: October 17, 1998.