Real valued functions and metric spaces quasi-isometric to trees

Details Real valued functions and metric spaces quasi-isometric to trees Real valued functions and metric spaces quasi-isometric to trees

2011-03-30

arxiv.org/abs/1103.5908v1

Mathematics

Geometric Topology

12 pages

Scientific paper

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.

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