On the Hausdorff dimension of ultrametric subsets in ℝⁿ James R. Lee, Manor Mendel, Mohammad Moharrami (2012) Fundamenta Mathematicae For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).