An invariant of bi-Lipschitz maps

Tom 143 / 1993

Hossein Movahedi-Lankarani Fundamenta Mathematicae 143 (1993), 1-9 DOI: 10.4064/fm-143-1-1-9


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.


  • Hossein Movahedi-Lankarani Department of Mathematics
    Penn State Altoona Campus
    Altoona, Pennsylvania 16601-3760

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