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Almost bi-Lipschitz embeddings and almost homogeneous sets
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Olson, Eric J. and Robinson, James C. (2010) Almost bi-Lipschitz embeddings and almost homogeneous sets. Transactions of the American Mathematical Society, Vol.362 (No.1). pp. 145-168. doi:10.1090/S0002-9947-09-04604-2 ISSN 0002-9947.
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Official URL: http://dx.doi.org/10.1090/S0002-9947-09-04604-2
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 bi-Lipschitz mapping (bi-Lipschitz 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 finite-dimensional 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 R-N are almost bi-Lipschitz between X and its image.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: | 0002-9947 | ||||
Official Date: | January 2010 | ||||
Dates: |
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Volume: | Vol.362 | ||||
Number: | No.1 | ||||
Number of Pages: | 24 | ||||
Page Range: | pp. 145-168 | ||||
DOI: | 10.1090/S0002-9947-09-04604-2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 8 December 2015 | ||||
Date of first compliant Open Access: | 8 December 2015 | ||||
Funder: | Royal Society (Great Britain) |
Data sourced from Thomson Reuters' Web of Knowledge
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