Abstract
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 these sufficient conditions are also necessary. Finally, we give an application to the existence of global implicit functions.
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O. Gutú and J. A. Jaramillo were supported in part by D.G.E.S. (Spain) Grant BFM2003-06420.
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Gutú, O., Jaramillo, J.A. Global homeomorphisms and covering projections on metric spaces. Math. Ann. 338, 75–95 (2007). https://doi.org/10.1007/s00208-006-0068-9
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DOI: https://doi.org/10.1007/s00208-006-0068-9