Almost Bi-lipschitz Embeddings and Almost Homogeneous Sets
نویسندگان
چکیده
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 (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 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 RN are almost bi-Lipschitz between X and its image.
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