The dual space of precompact groups

Abstract

For any topological group $G$ the dual object $\hat{G}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat{G}$ is discrete. In an earlier paper we proved that $\hat{G}$ 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.

8 pages. arXiv admin note: substantial text overlap with arXiv:1112.1350