Let and be two infinite-dimensional Banach spaces. If is crudely finitely representable in every finite-codimensional subspace of , then any proper subset of almost bi-Lipschitz embeds into , 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].
DOI : 10.5802/ambp.423
Keywords: Almost bi-Lipschitz, Banach space, embeddings, crudely finitely representable
Netillard, François 1
CC-BY 4.0
@article{AMBP_2024__31_1_1_0,
author = {Netillard, Fran\c{c}ois},
title = {Almost {bi-Lipschitz} embeddings and proper subsets of a {Banach} space - {An} extension of a {Theorem} by {M.I.} {Ostrovskii}},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {1--10},
year = {2024},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {31},
number = {1},
doi = {10.5802/ambp.423},
mrnumber = {4813802},
zbl = {07957315},
language = {en},
url = {https://www.numdam.org/articles/10.5802/ambp.423/}
}
TY - JOUR AU - Netillard, François TI - Almost bi-Lipschitz embeddings and proper subsets of a Banach space - An extension of a Theorem by M.I. Ostrovskii JO - Annales mathématiques Blaise Pascal PY - 2024 SP - 1 EP - 10 VL - 31 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://www.numdam.org/articles/10.5802/ambp.423/ DO - 10.5802/ambp.423 LA - en ID - AMBP_2024__31_1_1_0 ER -
%0 Journal Article %A Netillard, François %T Almost bi-Lipschitz embeddings and proper subsets of a Banach space - An extension of a Theorem by M.I. Ostrovskii %J Annales mathématiques Blaise Pascal %D 2024 %P 1-10 %V 31 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://www.numdam.org/articles/10.5802/ambp.423/ %R 10.5802/ambp.423 %G en %F AMBP_2024__31_1_1_0
Netillard, François. 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
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