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An invariant of bi-Lipschitz maps

100%

Movahedi-Lankarani H.

Fundamenta Mathematicae

1993

tom 143

nr 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.

Minimal bi-Lipschitz embedding dimension of ultrametric spaces

63%

Luukkainen J., Movahedi-Lankarani H.

Fundamenta Mathematicae

1994

tom 144

nr 2

181-193

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Movahedi-Lankarani H.

1 Luukkainen J.

1 1994

1 1993

Wyniki wyszukiwania

An invariant of bi-Lipschitz maps

Minimal bi-Lipschitz embedding dimension of ultrametric spaces