A hyperbolic metric space is a geometric structure in which the geometry is shaped by hyperbolic properties. More formally, a hyperbolic space is a geodesic metric space that satisfies certain conditions characterizing hyperbolic geometry, a non-Euclidean geometry. ### Key Characteristics: 1. **Negative Curvature**: Hyperbolic metric spaces have negative curvature.
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For , a geodesic metric space is -hyperbolic when each side of every metric geodesic triangle lies in the closed -neighbourhood of the other two sides.