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Analysis and Geometry in Metric Spaces

Ed. by Ritoré , Manuel

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CiteScore 2016: 0.04

SCImago Journal Rank (SJR) 2016: 0.110
Source Normalized Impact per Paper (SNIP) 2016: 0.026

Mathematical Citation Quotient (MCQ) 2016: 0.78


Emerging Science

Open Access
Online
ISSN
2299-3274
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A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension

Guy David
  • Univ Paris-Sud, Laboratoire de mathématiques UMR-8628, Orsay F-91405, France and Institut Universitaire de France
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/ Marie Snipes
Published Online: 2013-01-14 | DOI: https://doi.org/10.2478/agms-2012-0003

Abstract

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; dα ) ⃗ ℝ RN.

Keywords: Assouad Embedding; doubling metric spaces; snowflake distance

MSC: 53C23; 28A75; 54F45

  • P. Assouad, Plongements lipschitziens dans Rn, Bull. Soc. Math. France, 111(4), 429–448, 1983. Google Scholar

  • J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, 2001. Google Scholar

  • A. Naor and O. Neiman, Assouad’s theorem with dimension independent of the snowflaking, Revista Matemática Iberoamericana 28 (4), 1–21, 2012 Web of ScienceGoogle Scholar

About the article

Received: 2012-11-14

Accepted: 2012-12-26

Published Online: 2013-01-14


Citation Information: Analysis and Geometry in Metric Spaces, ISSN (Online) 2299-3274, DOI: https://doi.org/10.2478/agms-2012-0003.

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©2012 Versita Sp. z o.o.. This content is open access.

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