On Hilbertian subsets of finite metric spaces
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 \(\ell_ 2\).
scientific article; zbMATH DE number 4032352