-factorizable groups and subgroups of Lindelöf P-groups

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• 作者：Tkachenko ; M.
• 关键词：54H11 ; 22A05 ; 54G10 ; 54D20 ; 54G20 ; 54C10 ; 54C45 ; 54D60 ; R-Factorizable ; τ ; -Bounded ; Complete ; Lindelö ; f ; P-Space ; Realcompact ; Dieudonné ; -complete ; C-Embedded ; z-Embedded ; Weakly Lindelö ; f ; Lindelö
• 刊名：Topology and its Applications
• 出版年：2004
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：January 28, 2004
• 卷：136
• 期：1-3
• 页码：135-167
• 文件大小：371 K

摘要

The main subject of our study are P-groups, that is, the topological groups whose G_δ-sets are open. We establish several elementary properties of P-groups and then prove that a P-group is R-factorizable iff it is pseudo-ω₁-compact iff it is ω-stable. This characterization is used to show that direct products of R-factorizable P-groups as well as continuous homomorphic images of R-factorizable P-groups are R-factorizable. A special emphasis is placed on the study of subgroups of Lindelöf P-groups.