کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5778018 1633058 2017 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Local structure of Gromov-Hausdorff space, and isometric embeddings of finite metric spaces into this space
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Local structure of Gromov-Hausdorff space, and isometric embeddings of finite metric spaces into this space
چکیده انگلیسی
We investigate the geometry of the family M of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We show that sufficiently small neighborhoods of generic finite spaces in the subspace of all finite metric spaces with the same number of points are isometric to some neighborhoods in the space R∞N, i.e., in the space RN with the norm ‖(x1,…,xN)‖=maxi⁡|xi|. As a corollary, we get that each finite metric space can be isometrically embedded into M in such a way that its image belongs to a subspace consisting of all finite metric spaces with the same number k of points. If the initial space has n points, then one can take k as the least possible integer with n≤k(k−1)/2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 221, 15 April 2017, Pages 393-398
نویسندگان
, , ,