Ultrametric subsets with large Hausdorff dimension |
| |
| Authors: | Manor Mendel Assaf Naor |
| |
| Institution: | 1. Mathematics and Computer Science Department, Open University of Israel, 1 University Road, P.O. Box 808, Raanana, 43107, Israel
2. Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA
|
| |
| Abstract: | It is shown that for every ε∈(0,1), every compact metric space (X,d) has a compact subset S?X that embeds into an ultrametric space with distortion O(1/ε), and $$\dim_H(S)\geqslant (1-\varepsilon)\dim_H(X),$$ where dim H (?) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
