A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; d ) ⃗ ℝ R...

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Bibliographic Details
Published in:Analysis and Geometry in Metric Spaces 2013-01, Vol.1 (2013), p.36-41
Main Authors: David, Guy, Snipes, Marie
Format: Article
Language:English
Subjects:
28A75
53C23
54F45
Assouad Embedding
doubling metric spaces
snowflake distance
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Summary:We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; d ) ⃗ ℝ R
ISSN:2299-3274
2299-3274
DOI:10.2478/agms-2012-0003