It is shown that for every and there exist and with the following properties. For every metric space with doubling constant at most , the metric space admits a bi-Lipschitz embedding into with distortion at most . The classical Assouad embedding theorem makes the same assertion, but with as .
Cite this article
Assaf Naor, Ofer Neiman, Assouad’s theorem with dimension independent of the snowflaking. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1123–1142DOI 10.4171/RMI/706