Extending partial isometries |
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Authors: | Sławomir Solecki |
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Institution: | (1) Department of Mathematics, University of Illinois, 1409 W. Green St., 61801 Urbana, IL, USA |
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Abstract: | 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.
Research supported by NSF grant DMS-0400931. I would like to thank Ward Henson and Alekos Kechris for conversations and emails
regarding the paper. Part of this work was done when I visited Caltech in May 2004. I thank the mathematics department there
for support |
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