# The Apple Doesn’t Fall Far From the (Metric) Tree: Equivalence of Definitions

@article{Aksoy2013TheAD, title={The Apple Doesn’t Fall Far From the (Metric) Tree: Equivalence of Definitions}, author={Asuman G{\"u}ven Aksoy and Sixian Jin}, journal={arXiv: Metric Geometry}, year={2013} }

In this paper we prove the equivalence of definitions for metric trees and for \delta-hyperbolic spaces. We point out how these equivalences can be used to understand the geometric and metric properties of \delta-hyperbolic spaces and its relation to CAT(\kappa) spaces.

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