Global Homeomorphism and Covering Projections on Metric Spaces
Abstract
For a large class of metric spaces with nice local structure, which includes BanachFinsler 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 pathliftings 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 quasiisometric mappings, some of there sufficient conditions are also necessary. Finally, we give some applications to the existence of global implicit functions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606569
 Bibcode:
 2006math......6569G
 Keywords:

 Mathematics  Metric Geometry;
 58C15;
 58B20;
 46T05