High Quality Content by WIKIPEDIA articles! In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence.Gromov–Hausdorff distance measures how far two compact metric spaces are from being isometric. If X and Y are two compact metric spaces, then dGH (X,Y ) is defined to be the infimum of all numbers dH(f (X ), g (Y )) for all metric spaces M and all isometric embeddings f :X?M and g :Y?M. Here dH denotes Hausdorff distance between subsets in M and the isometric embedding is understood in the global sense, i.e it must preserve all distances, not only infinitesimally small ones; for example no compact Riemannian manifold of negative sectional curvature admits such an embedding into Euclidean space.

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