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].
Keywords: Almost bi-Lipschitz, Banach space, embeddings, crudely finitely representable
François Netillard 1
@article{AMBP_2024__31_1_1_0, author = {Fran\c{c}ois Netillard}, 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}, publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal}, volume = {31}, number = {1}, year = {2024}, doi = {10.5802/ambp.423}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.423/} }
TY - JOUR AU - François Netillard 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://ambp.centre-mersenne.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 François Netillard %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://ambp.centre-mersenne.org/articles/10.5802/ambp.423/ %R 10.5802/ambp.423 %G en %F AMBP_2024__31_1_1_0
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/
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