The weights of closed subgroups of a locally compact group
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Other documents of the author: Hernández, Salvador; Hofmann, Karl Heinrich; Morris, Sidney A.
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
The weights of closed subgroups of a locally compact groupDate
2012Publisher
Walter de GruyterISSN
1433-5883; 1435-444Bibliographic citation
J. Group Theory 15 (2012), 613–630Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionAbstract
Let G be an infinite locally compact group and let @ be a cardinal satisfying
@0 @ w.G/ for the weight w.G/ of G. It is shown that there is a closed subgroup
N of G with w.N / D @. Sample consequences are: (1) ... [+]
Let G be an infinite locally compact group and let @ be a cardinal satisfying
@0 @ w.G/ for the weight w.G/ of G. It is shown that there is a closed subgroup
N of G with w.N / D @. Sample consequences are: (1) Every infinite compact group
contains an infinite closed metric subgroup. (2) For a locally compact group G and @ a
cardinal satisfying @0 @ wloc.G/, where wloc.G/ is the local weight of G, there are
either no infinite compact subgroups at all or there is a compact subgroup N of G with
w.N / D @. (3) For an infinite abelian group G there exists a properly ascending family of
locally-quasiconvex group topologies on G, say, . @/@0 @ card.G/, such that .G; @/O OG. [-]
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Journal of Group Theory, 2012, Vol. 15, Num. 5Rights
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