Isometry groups of separable metric spaces-Reference-Cited by-同舟云学术

Isometry groups of separable metric spaces

Published:2009-01 Issue:1 Volume:146 Page:67-81
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

MALICKI MACIEJ,SOLECKI SŁAWOMIR

Abstract

AbstractWe show that every locally compact Polish group is isomorphic to the isometry group of a proper separable metric space. This answers a question of Gao and Kechris. We also analyze the natural action of the isometry group of a separable ultrametric space on the space. This leads us to a structure theorem representing an arbitrary separable ultrametric space as a bundle with an ultrametric base and with ultrahomogeneous fibers which are invariant under the action of the isometry group.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

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