On embeddings of locally finite metric spaces into ${\ell }_p$

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.

References in corpus (2)

• Coarse embeddability into Banach spaces
• Distortion in the finite determination result for embeddings of locally finite metric spaces into Banach spaces

Cited by in corpus (1)

• Generalized transportation cost spaces