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Almost biLipschitz embeddings and almost homogeneous sets
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Olson, Eric J. and Robinson, James C.. (2010) Almost biLipschitz embeddings and almost homogeneous sets. Transactions of the American Mathematical Society, Vol.362 (No.1). pp. 145168. ISSN 00029947

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Official URL: http://dx.doi.org/10.1090/S0002994709046042
Abstract
This paper is concerned with embeddings of homogeneous spaces into Euclidean spaces. We show that any homogeneous metric space can be embedded into a Hilbert space using an almost biLipschitz mapping (biLipschitz to within logarithmic corrections). The image of this set is no longer homogeneous, but 'almost homogeneous'. We therefore study the problem of embedding an almost homogeneous subset X of a Hilbert space H into a finitedimensional Euclidean space. We show that if X is a compact subset of a Hilbert space and X  X is almost homogeneous, then, for N sufficiently large, a prevalent set of linear maps from X into RN are almost biLipschitz between X and its image.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Mathematics 
Library of Congress Subject Headings (LCSH):  Embeddings (Mathematics), Hilbert space, Lipschitz spaces 
Journal or Publication Title:  Transactions of the American Mathematical Society 
Publisher:  American Mathematical Society 
ISSN:  00029947 
Official Date:  January 2010 
Volume:  Vol.362 
Number:  No.1 
Number of Pages:  24 
Page Range:  pp. 145168 
Identification Number:  10.1090/S0002994709046042 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Open Access 
Funder:  Royal Society (Great Britain) 
References:  1. P. Assouad Plongements lipschitziens dans Rn. Bulletin de la S. M. F. 111 (1983), 429–448. 
URI:  http://wrap.warwick.ac.uk/id/eprint/16573 
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