  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.
