It is proved that if an ultrametric space can be bi-Lipschitz embedded in , then its Assouad dimension is less than n. Together with a result of Luukkainen and Movahedi-Lankarani, where the converse was shown, this gives a characterization in terms of Assouad dimension of the ultrametric spaces which are bi-Lipschitz embeddable in .
@article{bwmeta1.element.bwnjournal-article-fmv150i1p25bwm,
author = {Kerkko Luosto},
title = {Ultrametric spaces bi-Lipschitz embeddable in $$\mathbb{R}$^n$
},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {25-42},
zbl = {0862.54024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p25bwm}
}
Luosto, Kerkko. Ultrametric spaces bi-Lipschitz embeddable in $ℝ^n$
. Fundamenta Mathematicae, Tome 149 (1996) pp. 25-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv150i1p25bwm/
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