  We prove that if X is a complete geodesic metric space with uniformly
generated first homology group and $f: X\to R$ is metrically proper on the
connected components and bornologous, then X is quasi-isometric to a tree.
  Using this and adapting the definition of hyperbolic approximation we obtain
an intrinsic sufficent condition for a metric space to be PQ-symmetric to an
ultrametric space.
