On hilbertian subsets of finite metric spaces
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The following result is proved: For everyε>0 there is aC(ε)>0 such that every finite metric space (X, d) contains a subsetY such that |Y|≧C(ε)log|X| and (Y, d Y) embeds (1 +ε)-isomorphically into the Hilbert spacel 2.
KeywordsHilbert Space Equivalence Relation Convex Body Euclidean Plane Absolute Constant
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- 1.A. Dvoretzky,Some results on convex bodies and Banach spaces, Proc. Int. Symp. on Linear Spaces, Jerusalem, 1961, pp. 123–160.Google Scholar