Real valued functions and metric spaces quasi-isometric to trees

Álvaro Martínez-Pérez

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arXiv · 1103.5908

Real valued functions and metric spaces quasi-isometric to trees

Álvaro Martínez-Pérez

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Abstract

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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BibTeX RIS

Álvaro Martínez-Pérez. 2011-03-30. Real valued functions and metric spaces quasi-isometric to trees. https://arxiv.org/abs/1103.5908

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