Geodesic
Minimal bi-Lipschitz embedding dimension of ultrametric spaces
Jouni Luukkainen1 ; Hossein Movahedi-Lankarani2
1Department of Mathematics P.O. Box 4 (Hallituskatu 15) FIN-00014 University of Helsinki Finland
2Department of Mathematics Penn State Altoona Altoona, PA 16601–3760 U.S.A.
Fundamenta Mathematicae, Tome 144 (1994) no. 2, pp. 181-193
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that an ultrametric space can be bi-Lipschitz embedded in $ℝ^n$ if its metric dimension in Assouad's sense is smaller than n. We also characterize ultrametric spaces up to bi-Lipschitz homeomorphism as dense subspaces of ultrametric inverse limits of certain inverse sequences of discrete spaces.
DOI : 10.4064/fm-144-2-181-193

Jouni Luukkainen   1   ; Hossein Movahedi-Lankarani  2

1 Department of Mathematics P.O. Box 4 (Hallituskatu 15) FIN-00014 University of Helsinki Finland
2 Department of Mathematics Penn State Altoona Altoona, PA 16601–3760 U.S.A. 
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Jouni Luukkainen ; Hossein Movahedi-Lankarani. Minimal bi-Lipschitz embedding dimension of ultrametric spaces. Fundamenta Mathematicae, Tome 144 (1994) no. 2, pp. 181-193. doi: 10.4064/fm-144-2-181-193

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