Duality properties of bounded torsion topological abelian groups

Abstract Let G be a precompact, bounded torsion abelian group and G p ∧ its dual group endowed with the topology of pointwise convergence. We prove that if G is Baire (resp., pseudocompact), then all compact (resp., countably compact) subsets of G p ∧ are finite. We also prove that G is pseudocompact if and only if all countable subgroups of G p ∧ are closed. We present other characterizations of pseudocompactness and the Baire property of G p ∧ in terms of properties that express in different ways the abundance of continuous characters of G . Besides, we give an example of a precompact boolean group G with the Baire property such that the dual group G p ∧ contains an infinite countably compact subspace without isolated points.