If G is a topological group with identity 1 and S 'subset or equal' G \{1}, then we say that S is a suitable set for G if (a) the subgroup <S> of G generated by S is dense in G, (b) S is relatively discrete, and (c) S \cup {1} is closed in G. We solve several open problems regarding the existence of (closed) suitable sets in some locally compact groups equipped with their Bohr topology and characterize the p-adic integers as well as other known compact finite-dimensional metrizable groups (Prodanov's class) within the class of countably compact Abelian groups by means of suitable sets.
Mathematics Subject Classification: 22A05, 22A10, 22B05, 22C05, 22D99, 54D30, 54E45, 54H11
Keywords: Bohr topology, (countably) compact group, metrizable group, Moore group, minimal group, Pontryagin-van Kampen duality, Prodanov's class, pseudocompact group, (closed, totally) suitable set, Takahashi group, totally bounded group, totally dense subgroup, transversal set
Date received: April 28, 1999.