: Mathématiques: hyperbolic metric space

geometry > non-Euclidean geometry > hyperbolic geometry > hyperbolic metric space

geometry > topological space > metric space > hyperbolic metric space

hyperbolic metric space

In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic groups.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Hyperbolic_metric_space)

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