On embeddings of locally finite metric spaces into $\ell_p$

Sofiya Ostrovska; Mikhail I. Ostrovskii

doi:10.1016/j.jmaa.2019.01.069

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arXiv · 1712.08255

On embeddings of locally finite metric spaces into $\ell_p$

Sofiya Ostrovska·Mikhail I. Ostrovskii

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Abstract

It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\le p\le \infty)$, then for every $\epsilon>0$, the space $M$ admits a $(C+\epsilon)$-bilipschitz embedding into $\ell_p$. The goal of this paper is to show that for $p\ne 2,\infty$ this result is sharp in the sense that $\epsilon$ cannot be dropped out of its statement.

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Sofiya Ostrovska, Mikhail I. Ostrovskii. 2017-12-21. On embeddings of locally finite metric spaces into $\ell_p$. https://doi.org/10.1016/j.jmaa.2019.01.069

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