The dual space of precompact groups

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