Geodesic
The dual space of precompact groups
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 239-244.

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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.
Classification : 22A25, 22C05, 22D35, 43A35, 43A40, 43A65, 54H11
Keywords: compact group; precompact group; representation; Pontryagin--van Kampen duality; compact-open topology; Fell dual space; Fell topology; Kazhdan property (T) 
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Ferrer, M.; Hernández, S.; Uspenskij, V. The dual space of precompact groups. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 239-244. http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a8/