2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113990For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We first obtain a general condition in terms of a path continuation property. As a consequence, we deduce several conditions in terms of path-liftings involving a generalized derivative, and in particular we obtain an extension of Hadamard global inversion theorem in this context. Next we prove that, in the case of quasi-isometric mappings, some of there sufficient conditions are also necessary. Finally, we give some applications to the existence of global implicit functions.Metric Geometry58C15,58B20,46T05text