Israel Journal of Mathematics

, Volume 150, Issue 1, pp 315–331 | Cite as

Extending partial isometries

  • Sławomir Solecki


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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Copyright information

© Hebrew University 2005

Authors and Affiliations

  • Sławomir Solecki
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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