Annales Mathématiques
Blaise Pascal
no. 1
Almost bi-Lipschitz embeddings and proper subsets of a Banach space - An extension of a Theorem by M.I. Ostrovskii
François Netillard1
1 Université de Franche-Comté, Laboratoire de Mathématiques UMR 6623, 16 route de Gray, 25030 Besançon Cedex, FRANCE.
Annales mathématiques Blaise Pascal, Tome 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].

Publié le :
DOI : 10.5802/ambp.423
Classification : 46B20, 46B85
Mots clés : 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.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 31 (2024) no. 1, pp. 1-10. doi : 10.5802/ambp.423. https://ambp.centre-mersenne.org/articles/10.5802/ambp.423/

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