In geometry, Alexandrov spaces with curvature ≥ k form a generalization of Riemannian manifolds with sectional curvature ≥ k, where k is some real number. By definition, these spaces are locally compact complete length spaces where the lower curvature bound is defined via comparison of geodesic triangles in the space to geodesic triangles in standard constant-curvature Riemannian surfaces. One can show that the Hausdorff dimension of an Alexandrov space with curvature ≥ k is either a non-negative integer or infinite. One can define a notion of "angle" and "tangent cone" in these spaces. Alexandrov...