Dieudonné Completion and PT-Groups
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Metadades
Títol
Dieudonné Completion and PT-GroupsData de publicació
2012-02Editor
Springer NetherlandsISSN
0927-2852Cita bibliogràfica
Applied Categorical Structures (2012), 20, 1, p. 1-18 (February 2012)Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://link.springer.com/article/10.1007/s10485-009-9208-1Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
We consider the classes of PT-groups, strong PT-groups, completion friendly groups, and Moscow groups introduced by Arhangel’skii for the study of the Dieudonné completion of topological groups. We show that every ... [+]
We consider the classes of PT-groups, strong PT-groups, completion friendly groups, and Moscow groups introduced by Arhangel’skii for the study of the Dieudonné completion of topological groups. We show that every subgroup H of a Lindelöf P-group is a PT-group, and that H is a strong PT-group iff it is R -factorizable. Assuming CH, we prove that every ω-narrow P-group is a PT-group. Several results regarding products of PT-groups and R -factorizable groups are established as well. We prove that the product of a Lindelöf group and an arbitrary subgroup of a Lindelöf Σ-group is completion friendly, and the same conclusion is valid for the product of an R -factorizable P-group with an almost metrizable group. [-]
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