TY - JOUR

T1 - Espaces métriques linéairement rigides

AU - Melleray, Julien

AU - Petrov, Fedor

AU - Vershik, Anatoly

PY - 2007/2/15

Y1 - 2007/2/15

N2 - It is a well-known fact that any metric space admits an isometric embedding into a Banach space (Kantorovitch-Monge embedding); here, we introduce and study the class of metric spaces which admit a unique (up to isometry) linearly dense embedding into a Banach space. We call these spaces linearly rigid. The first example of such a space was obtained by R. Holmes, who proved that the Urysohn space is linearly rigid. We provide a necessary and sufficient condition for a space to be linearly rigid. Then we discuss some corollaries, including new examples of linearly rigid metric spaces. To cite this article: J. Melleray et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

AB - It is a well-known fact that any metric space admits an isometric embedding into a Banach space (Kantorovitch-Monge embedding); here, we introduce and study the class of metric spaces which admit a unique (up to isometry) linearly dense embedding into a Banach space. We call these spaces linearly rigid. The first example of such a space was obtained by R. Holmes, who proved that the Urysohn space is linearly rigid. We provide a necessary and sufficient condition for a space to be linearly rigid. Then we discuss some corollaries, including new examples of linearly rigid metric spaces. To cite this article: J. Melleray et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).

UR - http://www.scopus.com/inward/record.url?scp=33846784048&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2006.12.015

DO - 10.1016/j.crma.2006.12.015

M3 - статья

AN - SCOPUS:33846784048

VL - 344

SP - 235

EP - 240

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 4

ER -