Duality properties of bounded torsion topological abelian groups

作者：Chasco M J; Dominguez X^*; Tkachenko M

来源：Journal of Mathematical Analysis and Applications, 2017, 448(2): 968-981.

DOI：10.1016/j.jmaa.2016.11.029

• Precompact group
• Baire property
• Pseudocompact
• Countably compact
• Pointwise convergence topology

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.

• 出版日期2017-4-15