کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4657862 | 1633078 | 2016 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the Borel complexity of characterized subgroups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
In a compact abelian group X, a subgroup H is called characterized if there exists a sequence of characters v=(vn)v=(vn) of X such that H={x∈X:vn(x)→0 in T}H={x∈X:vn(x)→0 in T}. Gabriyelyan proved for X=TX=T, that the characterized subgroup {x∈T:n!x→0 in T}{x∈T:n!x→0 in T} is not an FσFσ-set. In this paper, we obtain a complete description of the FσFσ-subgroups of TT characterized by sequences of integers v=(vn)v=(vn) such that vn|vn+1vn|vn+1 for all n∈Nn∈N showing that these are exactly the countable subgroups of TT. Moreover, in the general setting of compact metrizable abelian groups, we give a new point of view to study the Borel complexity of characterized subgroups in terms of appropriate test-topologies defined on the group X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 201, 15 March 2016, Pages 372–387
Journal: Topology and its Applications - Volume 201, 15 March 2016, Pages 372–387
نویسندگان
Dikran Dikranjan, Daniele Impieri,