Banach-Stone Theorems and Separating Maps.
The dual space of precompact groups
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. If is compact, is discrete. In an earlier paper we proved that 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 is an almost metrizable precompact group.
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