Linearly rigid metric spaces and the embedding problem

• Autorzy: J. Melleray , F. V. Petrov , A. M. Vershik
• Języki publikacji: EN

Abstrakty

EN

We consider the problem of isometric embedding of metric spaces into Banach spaces, and introduce and study the remarkable class of so-called linearly rigid metric spaces: these are the spaces that admit a unique, up to isometry, linearly dense isometric embedding into a Banach space. The first nontrivial example of such a space was given by R. Holmes; he proved that the universal Urysohn space has this property. We give a criterion of linear rigidity of a metric space, which allows us to give a simple proof of the linear rigidity of the Urysohn space and some other metric spaces. Various properties of linearly rigid spaces and related spaces are considered.

Kategorie tematyczne

• 51F10: Absolute spaces
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 199
• Numer: 2
• Strony: 177-194

Daty

wydano

2008

Twórcy

autor

J. Melleray

• UFR de Mathématiques, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

autor

F. V. Petrov

• Steklov Mathematical Institute at St. Petersburg, Fontanka 27, St. Petersburg 191023, Russia

autor

A. M. Vershik

• Steklov Mathematical Institute at St. Petersburg, Fontanka 27, St. Petersburg 191023, Russia

Identyfikatory

DOI

10.4064/fm199-2-6