Sequences and filters of characters characterizing subgroups of compact abelian groups
General Topology
2007-05-23 v2
Abstract
Let H be a countable subgroup of the metrizable compact abelian group G and f:H -> T=R/Z a (not necessarily continuous) character of H. Then there exists a sequence (chi_n)_n of (continuous) characters of G such that lim_n chi_n(alpha) = f(alpha) for all alpha in H and (chi_n(alpha))_n does not converge whenever alpha in G\H. If one drops the countability and metrizability requirement one can obtain similar results by using filters of characters instead of sequences. Furthermore the introduced methods allow to answer questions of Dikranjan et al.
Cite
@article{arxiv.math/0412447,
title = {Sequences and filters of characters characterizing subgroups of compact abelian groups},
author = {Mathias Beiglböck and Christian Steineder and Reinhard Winkler},
journal= {arXiv preprint arXiv:math/0412447},
year = {2007}
}
Comments
laTex2e, 10 pages