Global Homeomorphism and Covering Projections on Metric Spaces

Details Global Homeomorphism and Covering Projections on Metric Spaces Global Homeomorphism and Covering Projections on Metric Spaces

2006-06-22

arxiv.org/abs/math/0606569v1

Mathematics

Metric Geometry

Scientific paper

For 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.

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