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.

引用

页码：1 / 54

页数：54

共 40 条

[31]

Sagan H., 1994, Space-Filling Curves

[32] Two observations regarding embedding subsets of Euclidean spaces in normed spaces [J].