Almost bi-Lipschitz embeddings and proper subsets of a Banach space - An extension of a Theorem by M.I. Ostrovskii
Annales mathématiques Blaise Pascal, Volume 31 (2024) no. 1, pp. 1-10.

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 (see [1] and [2]). This is an extension of a result proved by M.I. Ostrovskii for locally finite subsets [9].

Published online:
DOI: 10.5802/ambp.423
Classification: 46B20, 46B85
Keywords: Almost bi-Lipschitz, Banach space, embeddings, crudely finitely representable

François Netillard 1

1 Université de Franche-Comté, Laboratoire de Mathématiques UMR 6623, 16 route de Gray, 25030 Besançon Cedex, FRANCE.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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François Netillard. Almost bi-Lipschitz embeddings and proper subsets of a Banach space - An extension of a Theorem by M.I. Ostrovskii. Annales mathématiques Blaise Pascal, Volume 31 (2024) no. 1, pp. 1-10. doi : 10.5802/ambp.423. https://ambp.centre-mersenne.org/articles/10.5802/ambp.423/

[1] Florent Baudier Barycentric gluing and geometry of stable metrics, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM, Volume 116 (2022) no. 1, 37, 48 pages | Zbl

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[8] François Netillard Plongements grossièrement Lipschitz et presque Lipschitz dans les espaces de Banach, Ph. D. Thesis, Université de Bourgogne Franche-Comté (2019) (https://theses.fr/2019UBFCD020, https://theses.hal.science/tel-02378971)

[9] Mikhail I. Ostrovskii Embeddability of locally finite metric spaces into Banach spaces is finitely determined, Proc. Am. Math. Soc., Volume 140 (2012) no. 8, pp. 2721-2730 | DOI | Zbl

[10] Mikhail I. Ostrovskii Metric embeddings: bilipschitz and coarse embeddings into Banach spaces, De Gruyter Studies in Mathematics, 49, Walter de Gruyter, 2013, xi+372 pages | DOI

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