Nondiscrete P-groups can be reflexive

作者：Galindo Jorge; Recoder Nunez Luis; Tkachenko Mikhail^*

来源：Topology and Its Applications, 2011, 158(2): 194-203.

DOI：10.1016/j.topol.2010.10.015

• Pontryagin's duality
• Reflexive
• P-group
• omega-bounded
• Product
• Sigma-product
• Compact subset
• Character depends on countably many coordinates

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 omega-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, Dominguez, 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.

• 出版日期2011-2-1