Intrinsic Timed Hausdorff Convergence and Its Implications

Abstract: Sakovich--Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov--Hausdorff distances and therefore extend naturally to a broader class of spaces. Here we show that, for timed metric spaces, intrinsic timed--Hausdorff convergence implies (timeless) Gromov--Hausdorff convergence as well as big bang convergence, among other related implications.