Ultrametric subsets with large Hausdorff dimension

被引：15
作者：
Mendel, Manor [1 ,3 ,4 ]
Naor, Assaf [2 ]
机构：
[1] Open Univ Israel, Dept Math & Comp Sci, IL-43107 Raanana, Israel
[2] NYU, Courant Inst, New York, NY 10012 USA
[3] Microsoft Res, Mountain View, CA USA
[4] Univ Washington, Seattle, WA 98195 USA
来源：
INVENTIONES MATHEMATICAE | 2013年 / 192卷 / 01期
关键词：
SPACES; SERVER; BOUNDS; SETS;
D O I：
10.1007/s00222-012-0402-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that for every epsilon a(0,1), every compact metric space (X,d) has a compact subset SaS dagger X that embeds into an ultrametric space with distortion O(1/epsilon), and dim(H) (S) >= (1 - epsilon) dim(H) (X), where dim (H) (.) denotes Hausdorff dimension. The above O(1/epsilon) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.
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收藏
页码：1 / 54
页数：54
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