  The null distance of Sormani and Vega encodes the manifold topology as well
as the causality structure of a (smooth) spacetime. We extend this concept to
Lorentzian length spaces, the analog of (metric) length spaces, which
generalize Lorentzian causality theory beyond the manifold level. We then study
Gromov-Hausdorff convergence based on the null distance in warped product
Lorentzian length spaces and prove first results on its compatibility with
synthetic curvature bounds.
