M. Ferrer, S. Hernández, V. Uspenskij
The dual space of precompact groups

Comment.Math.Univ.Carolin. 54,2 (2013) 239-244.

Abstract:For any topological group $G$ the dual object $\widehat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\widehat G$ is discrete. In an earlier paper we proved that $\widehat G$ is discrete for every metrizable precompact group, i.e.~a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.

Keywords: compact group, precompact group, representation, Pontryagin--van Kampen duality, compact-open topology, Fell dual space, Fell topology, Kazhdan property (T)
AMS Subject Classification: 43A40 22A25 22C05 22D35 43A35 43A65 54H11