Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 37, 2012, 525-538
Universidad de Castilla-La Mancha, Departamento de Análisis Económico y Finanzas
Talavera de la Reina, 45600 Toledo, Spain; alvaro.martinezperez 'at' uclm.es
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.
2010 Mathematics Subject Classification: Primary 54E35, 53C23; Secondary 20F65.
Key words: Quasi-isometry, tree, hyperbolic approximation, PQ-symmetric.
Reference to this article: Á. Martínez-Pérez: Real valued functions and metric spaces quasi-isometric to trees. Ann. Acad. Sci. Fenn. Math. 37 (2012), 525-538.
doi:10.5186/aasfm.2012.3734
Copyright © 2012 by Academia Scientiarum Fennica