Sequences and filters of characters characterizing subgroups of compact abelian groups

Details Sequences and filters of characters characterizing subgroups of compact abelian groups Sequences and filters of characters characterizing subgroups of compact abelian groups

2004-12-22

arxiv.org/abs/math/0412447v2

Mathematics

General Topology

laTex2e, 10 pages

Scientific paper

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.

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