Real valued functions and metric spaces quasi-isometric to trees

الأصل · EN

We prove that if X is a complete geodesic metric space with uniformly generated first homology group and f: X→ 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.