Extending partial isometries

SŁawomir Solecki

Research output: Contribution to journalArticlepeer-review


We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. 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.

Original languageEnglish (US)
Pages (from-to)315-331
Number of pages17
JournalIsrael Journal of Mathematics
StatePublished - 2005

ASJC Scopus subject areas

  • Mathematics(all)


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