A constructive proof of the Assouad embedding theorem with bounds on the dimension

We give a constructive proof of a theorem of Naor and Neiman, (to appear, Revista Matematica Iberoamercana), which asserts that if \((E,d)\) is a doubling metric space, there is an integer \(N > 0\), that depends only on the metric doubling constant, such that for each exponent \(\alpha \in (1/2,...

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Bibliographic Details
Published in:arXiv.org 2012-11
Main Authors: Guy, David, Snipes, Marie
Format: Article
Language:English
Subjects:
Mapping
Metric space
Theorem proving
Theorems
Online Access:Get full text
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Summary:We give a constructive proof of a theorem of Naor and Neiman, (to appear, Revista Matematica Iberoamercana), which asserts that if \((E,d)\) is a doubling metric space, there is an integer \(N > 0\), that depends only on the metric doubling constant, such that for each exponent \(\alpha \in (1/2,1)\), we can find a bilipschitz mapping \(F = (E,d^{\alpha}) \to \R^N\).
ISSN:2331-8422