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Geodesic metric space

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In mathematics, a geodesic metric space, or a geodesic space, is a concept in metric geometry and metric space theory that formalizes the idea of a space in which any two points can be joined by a shortest path lying entirely in the space. Geodesic metric spaces generalize the notion of straight line segments in Euclidean space and geodesics on a Riemannian manifold to arbitrary metric spaces, without requiring smooth or linear structure.