A Simple Proof of Dvoretzky-Type Theorem for Hausdorff Dimension in Doubling Spaces
نویسندگان
چکیده
The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type for Hausdorff dimension: For any $0<\beta<\alpha$, compact metric space $X$ of dimension $\alpha$ contains a subset which is biLipschitz equivalent to an and has at least $\beta$. In this note we present simple proof in doubling spaces using Bartal's Ramsey decompositions [Bartal 2021]. same general approach also used answer question Zindulka [Zindulka 2020] about existence "nearly ultrametric" subsets having full dimension.
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ژورنال
عنوان ژورنال: Analysis and Geometry in Metric Spaces
سال: 2022
ISSN: ['2299-3274']
DOI: https://doi.org/10.1515/agms-2022-0133