Almost bi--Lipschitz embeddings using covers of balls centred at the\n origin

2020/01/08 by Alexandros Margaris, Margaris, Alexandros
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2001.02607

openalex publication_date 2020/01/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In 2010, Olson & Robinson [Transactions of the American Mathematical\nSociety, 362(1), 145-168] introduced the notion of an almost homogeneous metric\nspace and showed that if X is a subset of a Hilbert space such that X-X is\nalmost homogeneous, then X admits almost bi--Lipschitz embeddings into\nEuclidean spaces. In this paper, we extend this result and we show that if X\nis a subset of a Banach space such that X-X is almost homogeneous at the\norigin, then X can be embedded in a Euclidean space in an almost\nbi--Lipschitz way.\n

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