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arXiv math/04124472004-12math.GN

刻画紧阿贝尔群子群的特征标序列和滤子

Sequences and filters of characters characterizing subgroups of compact abelian groups

Mathias Beiglböck, Christian Steineder, Reinhard Winkler

备注：: laTex2e, 10 pages

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摘要：

设H是可度量化紧阿贝尔群G的可数子群，f：H -> T=R/Z是H的特征标.则存在G的（连续）特征标序列（chi_n）_n，使得对H中的所有α，lim_nchi_n（alpha）= f（alpha），且（chi_n（alpha））_n不收敛于G \H中的任何α.如果放弃可数性和度量性要求，可以通过使用字符过滤器而不是序列来获得类似的结果。此外，介绍的方法允许回答问题的Dikranjan等人。

英文摘要：

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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