Resumen:
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. (C) 2016 Elsevier Inc. All rights reserved.