Duality properties of bounded torsion topological abelian groups

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• 作者：M.J. Chasco^a ; ^{mjchasco@unav.es} ; X. Domí ; nguez^b ; ^{xabier.dominguez@udc.es} ; M. Tkachenko^c ; ^{mich@xanum.uam.mx}
• 关键词：Precompact group ; Baire property ; Pseudocompact ; Countably compact ; Pointwise convergence topology
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：968-981
• 全文大小：439 K
• 卷排序：448

文摘

Let G   be a precompact, bounded torsion abelian group and Gp∧ 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 Gp∧ are finite. We also prove that G   is pseudocompact if and only if all countable subgroups of Gp∧ are closed. We present other characterizations of pseudocompactness and the Baire property of Gp∧ 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 Gp∧ contains an infinite countably compact subspace without isolated points.