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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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