## Are ultralimits the Gromov-Hausdorff limits of a subsequence?

Let (Mi,pi) be a sequence of n-dimensional Riemannian manifolds with lower Ricci curvature bound −1. Fix a non-orincipal ultrafilter and let X be the ultralimit of the sequence. Does there exists a p∈X and subsequence of (Mi,pi) converging to (X,p) in the pointed Gromov-Hausdorff sense? Answer AttributionSource : Link , Question Author : dg.jan , … Read more