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

الأصل · EN

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.