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Linearly rigid metric spaces and the embedding problem

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Melleray J., Petrov F., Vershik A.

Fundamenta Mathematicae

2008

tom 199

nr 2

177-194

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Melleray J.

1 Petrov F.

1 Vershik A.

1 2008

Wyniki wyszukiwania

Linearly rigid metric spaces and the embedding problem