Nondiscrete P-groups can be reflexive

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• 作者：Jorge Galindo ; Luis Recoder-Nú ; ñ ; ez ; Mikhail Tkachenko
• 关键词：Pontryagin's duality ; Reflexive ; P-group ; ω ; -bounded ; Product ; Σ ; -product ; Compact subset ; Character depends on countably many coordinates
• 刊名：Topology and its Applications
• 出版年：2011
• 出版时间：1 February 2011
• 年：2011
• 卷：158
• 期：2
• 页码：194-203
• 全文大小：209 K

文摘

We present the first examples of nondiscrete reflexive P-groups (topological groups in which countable intersections of open sets are open) as well as of noncompact reflexive ω-bounded groups (precompact groups in which the closure of every countable set is compact). Our main result implies that every product of discrete Abelian groups equipped with the P-modified topology is reflexive. Taking uncountably many nontrivial factors, we thus answer a question posed by P. Nickolas and solve a problem raised by Ardanza-Trevijano, Chasco, Domínguez, and Tkachenko.

New examples of non-reflexive P-groups are also given which are based on a further development of Leptin's technique going back to 1955.