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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On the Borel complexity of characterized subgroups
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
نویسندگان
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