Extending partial isometries | Zendy

Sławomir Solecki | Zendy

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Extending partial isometries

Author(s) -

Sławomir Solecki

Publication year - 2005

Publication title -

israel journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.168

H-Index - 63

eISSN - 1565-8511

pISSN - 0021-2172

DOI - 10.1007/bf02762385

Subject(s) - isometry (riemannian geometry) , mathematics , metric space , isometry group , metric (unit) , injective metric space , convex metric space , pure mathematics , extension (predicate logic) , space (punctuation) , intrinsic metric , metric differential , computer science , operations management , economics , programming language , operating system

We show that a finite metric spaceA admits an extension to a finite metric spaceB so that each partial isometry ofA extends to an isometry ofB. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.

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