Nondiscrete P-groups can be reflexive
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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http://dx.doi.org/10.1016/j.topol.2010.10.015 |
Metadata
Title
Nondiscrete P-groups can be reflexiveDate
2011-02-01Publisher
ElsevierISSN
0166-8641Bibliographic citation
Topology and its Applications (Feb. 2011), vol. 158, no. 2, p. 194-203Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0166864110003366Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
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 ... [+]
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. [-]
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© 2011 Elsevier Inc. All rights reserved
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- MAT_Articles [765]