Problem. Does every compact metric space of finite packing dimension admit a bi-Lipschitz embedding into the Hilbert space $ \ell_2$ ? The packing dimension of a compact metric space $ (X,d)$ in the (finite or infinite) number $ $ Dim(X)=\limsup_{\varepsilon\to 0}\frac{\ln N_\varepsilon(X)}{\ln(1/\varepsilon)},$ $ where $ N_\varepsilon(X)$ is the cardinality of the smallest cover of $Read more