Embedding proper ultrametric spaces into $\ell_p$ and its application to nonlinear Dvoretzky's theorem

Details Embedding proper ultrametric spaces into $\ell_p$ and its application to nonlinear Dvoretzky's theorem Embedding proper ultrametric spaces into $\ell_p$ and its application to nonlinear Dvoretzky's theorem

2012-03-08

arxiv.org/abs/1203.1761v1

Mathematics

Metric Geometry

6 pages

Scientific paper

We prove that every proper ultrametric space isometrically embeds into
$\ell_p$ for any $p\geq 1$. As an application we discuss an $\ell_p$-version of
nonlinear Dvoretzky's theorem.

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