Almost bi-Lipschitz embeddings and proper subsets of a Banach space -- An extension of a theorem by M.I. Ostrovskii

2022/09/23 by François Netillard, Netillard, François
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2209.11828

openalex publication_date 2022/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X and Y be two infinite-dimensional Banach spaces. If X is crudely finitely representable in every finite-codimensional subspace of Y, then any proper subset of X almost bi-Lipschitz embeds into Y, in a sense quite close to that of F. Baudier and G. Lancien. This is an extension of a result proved by M.I. Ostrovskii for locally finite subsets.

Related

• Almost bi--Lipschitz embeddings using covers of balls centred at the\n origin
• Best constants for Lipschitz embeddings of metric spaces into c₀
• Regular mappings and non-existence of bi-Lipschitz embeddings for slit carpets
• On embeddings of finite subsets of ℓ₂
• On the extension of bi-Lipschitz mappings