Reflexivity in precompact groups and extensions
Visualitza/
Impacte
Scholar |
Altres documents de l'autoria: Galindo, Jorge; Tkachenko, Mikhail; Bruguera, Montserrat; Hernández, Constancio
Metadades
Mostra el registre complet de l'elementcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadades
Títol
Reflexivity in precompact groups and extensionsData de publicació
2014-02Editor
ElsevierCita bibliogràfica
GALINDO, J., et al. Reflexivity in precompact groups and extensions. Topology and its Applications, 2014, 163: 112-127.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0166864113003842Versió
info:eu-repo/semantics/sumittedVersionParaules clau / Matèries
Resum
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). [-]
Publicat a
Topology and its Applications Volume 163, 15 February 2014Drets d'accés
Copyright © 2015 Elsevier B.V. or its licensors or contributors.
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
Apareix a les col.leccions
- MAT_Articles [751]