کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4667763 | 1345477 | 2007 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Graev metric groups and Polishable subgroups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We prove a conjecture of Hjorth: There is an uncountable Polish group all of whose abelian subgroups are discrete. We first construct directly a witness to Hjorth's conjecture. Then we consider an existing example in the literature. The example is the metric completion of a free topological group constructed by Graev. We give a definition slightly more general than Graev's and prove some properties of the Graev metrics which seem to be unknown previously. We also consider the problem of finding Polishable subgroups of the Graev metric groups with arbitrarily high Borel rank. In doing this we prove some general theorems on extensions of Polish groups with this property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 213, Issue 2, 20 August 2007, Pages 887-901
Journal: Advances in Mathematics - Volume 213, Issue 2, 20 August 2007, Pages 887-901