Duality properties of bounded torsion topological abelian groups (Q730209)

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.