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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).
Переведенное название | Linearly rigid metric spaces |
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Язык оригинала | французский |
Страницы (с-по) | 235-240 |
Число страниц | 6 |
Журнал | Comptes Rendus Mathematique |
Том | 344 |
Номер выпуска | 4 |
DOI | |
Состояние | Опубликовано - 15 фев 2007 |
ID: 49850432