کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661471 | 1344429 | 2007 | 22 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On minimal non-potentially closed subsets of the plane
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
We study the Borel subsets of the plane that can be made closed by refining the Polish topology on the real line. These sets are called potentially closed. We first compare Borel subsets of the plane using products of continuous functions. We show the existence of a perfect antichain made of minimal sets among non-potentially closed sets. We apply this result to graphs, quasi-orders and partial orders. We also give a non-potentially closed set minimum for another notion of comparison. Finally, we show that we cannot have injectivity in the Kechris–Solecki–Todorčević dichotomy about analytic graphs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 1, 1 January 2007, Pages 241-262
Journal: Topology and its Applications - Volume 154, Issue 1, 1 January 2007, Pages 241-262