Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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.
Язык оригинала | английский |
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Страницы (с-по) | 177-194 |
Число страниц | 18 |
Журнал | Fundamenta Mathematicae |
Том | 199 |
Номер выпуска | 2 |
DOI | |
Состояние | Опубликовано - 2 июл 2008 |
ID: 47858966