Abstract
We show that every compact ultrametric space is bi-Lipschitz embeddable in a Hilbert space. We also provide an example of a compact ultrametric space whose fractal (and hence Hausdorff) dimension is finite, but which cannot be bi-Lipschitz embedded in any finite dimensional Euclidean space. This example, in particular, establishes that the inverse of Mañé’s projection need not be Lipschitz even in the case of finite fractal dimension.
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