Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 62, No. 3, pp. 247-268 (2005)

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On bi-Lipschitz embeddings

H. Movahedi-Lankarani and R. Wells

Department of Mathematics and Statistics, Penn State Altoona,
Altoona, PA 16601-3760 -- USA
E-mail: hml@math.psu.edu
Department of Mathematics, Penn State University,
University Park, PA 16802 -- USA
E-mail: wells@math.psu.edu

Abstract: Let $\mu$ be a finite Borel regular measure on a compact metric space $(X,\rho)$, nontrivial on nonempty open sets. It is shown that whenever the map $\iota_{\rho}: X\to L^p(\mu)$ given by $\iota_{\rho}(x)=\rho(x,\cdot)$ is lower Lipschitz for some $1<p<\infty$, then there is a bi-Lipschitz embedding of $(X,\rho)$ into some $\R^N$.

Keywords: Lipschitz; bilipschitz; bi-Lipschitz; embedding; spherically compact; canonical map; evaluation map.

Classification (MSC2000): 54E40, 58C20.; 54C25, 54F45, 54F50, 58C25, 57R35, 57R40, 26B05.

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Electronic version published on: 7 Mar 2008.

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