A constructive proof of the Assouad embedding theorem with bounds on the dimension

We give a constructive proof of a theorem of Naor and Neiman, (to appear, Revista Matematica Iberoamercana), which asserts that if $(E,d)$ is a doubling metric space, there is an integer $N > 0$, that depends only on the metric doubling constant, such that for each exponent $α\in (1/2,1)$, we can find a bilipschitz mapping $F = (E,d^α) \to \R^N$.

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