On Hilbertian subsets of finite metric spaces (Q1096846)
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scientific article; zbMATH DE number 4032352
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hilbertian subsets of finite metric spaces |
scientific article; zbMATH DE number 4032352 |
Statements
On Hilbertian subsets of finite metric spaces (English)
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1986
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The following result is proved: For every \(\epsilon >0\) there is a \(C(\epsilon)>0\) such that every finite metric space (X,d) contains a subset Y such that \(| Y| \geq C(\epsilon)\log | X|\) and \((Y,d_ Y)\) embeds \((1+\epsilon)\)-isomorphically into the Hilbert space \(\ell_ 2\).
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