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Duality properties of bounded torsion topological abelian groups. (English) Zbl 1359.22001
This article mainly discusses the pseudocompactness and the Baire property of the dual group $$G^{\wedge}_{p}$$ of a precompact bounded torsion abelian topological group $$G$$, where the group $$G^{\wedge}_{p}$$ of continuous characters of $$G$$ is endowed with the topology of pointwise convergence. In particular, the authors prove that if $$G$$ is pseudocompact (Baire), then countably compact (compact) subsets of $$G^{\wedge}_{p}$$ are finite. Also, the authors present an example of a precompact Boolean group $$G$$ with the Baire property such that the dual group $$G^{\wedge}_{p}$$ contains an infinite countably compact subspace without isolated points.

##### MSC:
 22A05 Structure of general topological groups 54E52 Baire category, Baire spaces
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##### References:
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