Sequences and filters of characters characterizing subgroups of compact abelian groups

2004/12/22 by Mathias Beiglböck, Beiglböck, Mathias, Christian Steineder +4
Computer Science · Mathematics · #22C05 #54H11 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #General Topology (math.GN) #advanced mathematical theories #math.GN #msc:22C05 #msc:54H11

paper · pdf · doi:10.48550/arxiv.math/0412447

laTex2e, 10 pages

openalex publication_date 2004/12/22 · arxiv created 2005/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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