کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658172 | 1633084 | 2015 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A pseudometric invariant under similarities in the hyperspace of non-degenerated compact convex sets of Rn
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this work we define a new pseudometric in Kân, the hyperspace of all non-degenerated compact convex sets of Rn, which is invariant under similarities. We will prove that the quotient space generated by this pseudometric (which is the orbit space generated by the natural action of the group of similarities on Kân) is homeomorphic to the Banach-Mazur compactum BM(n), while Kân is homeomorphic to the topological product QÃRn+1, where Q stands for the Hilbert cube. Finally we will show some consequences in convex geometry, namely, we measure how much two convex bodies differ (by means of our new pseudometric) in terms of some classical functionals.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 194, October 2015, Pages 125-143
Journal: Topology and its Applications - Volume 194, October 2015, Pages 125-143
نویسندگان
Bernardo González Merino, Natalia Jonard-Pérez,