Gromov–Hausdorff convergence

Summary

Gromov–Hausdorff convergence is a notion of convergence for sequences of metric spaces, not of points inside one space. A sequence of compact metric spaces converges when its distance to the limit in the Gromov–Hausdorff space tends to zero. It lets one take limits of Riemannian manifolds, and such limits are often singular spaces. It is a basic tool of metric and synthetic methods in global geometry.