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
