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Title: Connected LCA groups are sequentially connected (English)
Author: Lin, Shou
Author: Tkachenko, Mikhail
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 54
Issue: 2
Year: 2013
Pages: 263-272
Summary lang: English
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Category: math
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Summary: We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if $H$ is a connected locally compact Abelian subgroup of a Hausdorff topological group $G$ and the quotient space $G/H$ is sequentially connected, then so is $G$. (English)
Keyword: locally compact
Keyword: connected
Keyword: sequentially connected
Keyword: Pontryagin duality
Keyword: torsion-free
Keyword: divisible
Keyword: metrizable element
Keyword: extension of a group
MSC: 22A30
MSC: 22D35
MSC: 54A25
MSC: 54D30
MSC: 54H10
MSC: 54H11
idZBL: Zbl 06221268
idMR: MR3067709
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Date available: 2013-06-25T12:56:29Z
Last updated: 2015-07-06
Stable URL: http://hdl.handle.net/10338.dmlcz/143275
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