Pontryagin duality in the class of precompact Abelian groups and the Baire property

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• 作者：M. Bruguera ; M. Tkachenko
• 关键词：Primary ; 43A40 ; 22D35 ; Secondary ; 22C05 ; 54E52 ; 54C10
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 出版时间：December, 2012
• 年：2012
• 卷：216
• 期：12
• 页码：2636-2647
• 全文大小：290 K

文摘

We present a wide class of reflexive, precompact, non-compact, Abelian topological groups determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group are finite. We also show that many (non-reflexive) precompact Abelian groups are quotients of reflexive precompact Abelian groups. This includes all precompact almost metrizable groups with the Baire property and their products. Finally, given a compact Abelian group of weight , we find proper dense subgroups and of such that is reflexive and pseudocompact, while is non-reflexive and almost metrizable.