On Embeddings of Locally Finite Metric Spaces Into <i>l<sub>p</Sub><

Abstract

It is known that if finite subsets of a locally finite metric space M admit C-bilipschitz embeddings into l(p) (1 <= p <= infinity), then for every epsilon > 0, the space M admits a (C + epsilon)-bilipschitz embedding into l(p). The goal of this paper is to show that for p not equal 2, infinity this result is sharp in the sense that e cannot be dropped out of its statement. (C) 2019 Elsevier Inc. All rights reserved.