The dual space of precompact groups

Abstract

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