کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661401 | 1344427 | 2006 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the Steinhaus property in topological groups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let G be a locally compact Abelian group and μ a Haar measure on G. We prove: (a) If G is connected, then the complement of a union of finitely many translates of subgroups of G with infinite index is μ-thick and everywhere of second category. (b) Under a simple (and fairly general) assumption on G, for every cardinal number m such that ℵ0⩽m⩽|G| there is a subgroup of G of index m that is μ-thick and everywhere of second category. These results extend theorems by Muthuvel and Erdős–Marcus, respectively. (b) also implies a recent theorem by Comfort–Raczkowski–Trigos stating that every nondiscrete compact Abelian group G admits 2|G|-many μ-nonmeasurable dense subgroups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issue 12, 1 June 2006, Pages 2035-2046
Journal: Topology and its Applications - Volume 153, Issue 12, 1 June 2006, Pages 2035-2046