An invariant of bi-Lipschitz maps
Volume 143 / 1993
Fundamenta Mathematicae 143 (1993), 1-9
DOI: 10.4064/fm-143-1-1-9
Abstract
A new numerical invariant for the category of compact metric spaces and Lipschitz maps is introduced. This invariant takes a value less than or equal to 1 for compact metric spaces that are Lipschitz isomorphic to ultrametric ones. Furthermore, a theorem is provided which makes it possible to compute this invariant for a large class of spaces. In particular, by utilizing this invariant, it is shown that neither a fat Cantor set nor the set ${0}∪{1/n}_{n≥1}$ is Lipschitz isomorphic to an ultrametric space.
