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

2009/11/01 by Manoussos, Antonios
#37B05 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.0911.0154

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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