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 is Lipschitz isomorphic to an ultrametric space.
@article{bwmeta1.element.bwnjournal-article-fmv143i1p1bwm,
author = {Hossein Movahedi-Lankarani},
title = {An invariant of bi-Lipschitz maps},
journal = {Fundamenta Mathematicae},
volume = {142},
year = {1993},
pages = {1-9},
zbl = {0845.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv143i1p1bwm}
}
Movahedi-Lankarani, Hossein. An invariant of bi-Lipschitz maps. Fundamenta Mathematicae, Tome 142 (1993) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv143i1p1bwm/
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