Assouad’s Theorem with Dimension Independent of the Snowflaking
نویسنده
چکیده
It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, the metric space (X, d1−ε) admits a bi-Lipschitz embedding into R with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε→ 0.
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