Salvador Hernández, Karl H. Hofmann, Sidney A. Morris
September 1, 2012
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 .