Reflexivity of prodiscrete topological groups
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONAquest recurs és restringit
http://dx.doi.org/10.1016/j.jmaa.2011.05.063 |
Metadades
Títol
Reflexivity of prodiscrete topological groupsData de publicació
2011Editor
ElsevierISSN
0022-247XCita bibliogràfica
Journal of Mathematical Analysis and Applications (Dec. 2011) vol. 384, no. 2, p. 320-330Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0022247X11005154Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
We study the duality properties of two rather different classes of subgroups of direct products of discrete groups (protodiscrete groups): P-groups, i.e., topological groups such that countable intersections of its ... [+]
We study the duality properties of two rather different classes of subgroups of direct products of discrete groups (protodiscrete groups): P-groups, i.e., topological groups such that countable intersections of its open subsets are open, and protodiscrete groups of countable pseudocharacter (topological groups in which the identity is the intersection of countably many open sets). It was recently shown by the same authors that the direct product Π of an arbitrary family of discrete Abelian groups becomes reflexive when endowed with the ω-box topology. This was the first example of a non-discrete reflexive P-group. Here we present a considerable generalization of this theorem and show that every product of feathered (equivalently, almost metrizable) Abelian groups equipped with the P-modified topology is reflexive. In particular, every locally compact Abelian group with the P-modified topology is reflexive. We also examine the reflexivity of dense subgroups of products Π with the P-modified topology and obtain the first examples of non-complete reflexive P-groups. We find as well that the better behaved class of prodiscrete groups (complete protodiscrete groups) of countable pseudocharacter contains non-reflexive members—any uncountable bounded torsion Abelian groupG of cardinality ω2 supports a topology τ such that (G,τ) is a non-reflexive prodiscrete group of countable pseudocharacter. [-]
Drets d'accés
© 2011 Elsevier Inc. All rights reserved
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/restrictedAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/restrictedAccess
Apareix a les col.leccions
- MAT_Articles [766]