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The group of isometries of a locally compact metric space with one end

Authors
  • Manoussos, Antonios
Type
Preprint
Publication Date
Sep 27, 2010
Submission Date
Nov 01, 2009
Identifiers
arXiv ID: 0911.0154
Source
arXiv
License
Yellow
External links

Abstract

In this note we study the dynamics of the natural evaluation action of the group of isometries $G$ of a locally compact metric space $(X,d)$ with one end. Using the notion of pseudo-components introduced by S. Gao and A. S. Kechris we show that $X$ has only finitely many pseudo-components of which exactly one is not compact and $G$ acts properly on. The complement of the non-compact component is a compact subset of $X$ and $G$ may fail to act properly on it.

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