Sequences and filters of characters characterizing subgroups of compact abelian groups
نویسندگان
چکیده
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 (χn) ∞ n=1 of (continuous) characters of G such that limn→∞ χn(α) = f(α) for all α ∈ H and (χn(α)) ∞ n=1 does not converge whenever α ∈ 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. MSC: 22C05; 43A40; 54A20
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