Reflexivity of prodiscrete topological groups
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
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http://dx.doi.org/10.1016/j.jmaa.2011.05.063 |
Metadatos
Título
Reflexivity of prodiscrete topological groupsFecha de publicación
2011Editor
ElsevierISSN
0022-247XCita bibliográfica
Journal of Mathematical Analysis and Applications (Dec. 2011) vol. 384, no. 2, p. 320-330Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.sciencedirect.com/science/article/pii/S0022247X11005154Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. [-]
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