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Publicly Available Published by De Gruyter September 1, 2012

The weights of closed subgroups of a locally compact group

  • Salvador Hernández EMAIL logo , Karl H. Hofmann and Sidney A. Morris
From the journal Journal of Group Theory

Abstract.

Let G be an infinite locally compact group and let be a cardinal satisfying for the weight of G. It is shown that there is a closed subgroup N of G with . 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 , where 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 . (3) For an infinite abelian group G there exists a properly ascending family of locally-quasiconvex group topologies on G, say, , such that .

Received: 2012-01-14
Revised: 2012-04-06
Published Online: 2012-09-01
Published in Print: 2012-09-01

© 2012 by Walter de Gruyter Berlin Boston

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