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compact group; precompact group; representation; Pontryagin--van Kampen duality; compact-open topology; Fell dual space; Fell topology; Kazhdan property (T)
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.
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