X-Nico

unusual facts about Hausdorff dimension


Metric dimension

Hausdorff dimension, an extended non-negative real number associated with any metric space that generalizes the notion of the dimension of a real vector space


Quasisymmetric map

For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ℝ.


see also