Reflexivity in precompact groups and extensions
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Other documents of the author: Galindo, Jorge; Tkachenko, Mikhail; Bruguera, Montserrat; Hernández, Constancio
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comunitat-uji-handle3:10234/8635
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Title
Reflexivity in precompact groups and extensionsDate
2014-02Publisher
ElsevierBibliographic citation
GALINDO, J., et al. Reflexivity in precompact groups and extensions. Topology and its Applications, 2014, 163: 112-127.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0166864113003842Version
info:eu-repo/semantics/sumittedVersionSubject
Abstract
We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that:
(1)
A precompact Abelian group G ... [+]
We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that:
(1)
A precompact Abelian group G of bounded order is reflexive iff the dual group G∧G∧ has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G.
(2)
Any extension of a reflexive P-group by another reflexive P-group is again reflexive.
We show on the other hand that an extension of a compact group by a reflexive ω-bounded group (even dual to a reflexive P-group) can fail to be reflexive.
We also show that the P-modification of a reflexive σ-compact group can be non-reflexive (even if, as proved in [20], the P-modification of a locally compact Abelian group is always reflexive). [-]
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Topology and its Applications Volume 163, 15 February 2014Rights
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