Mathematische Annalen

, 338:75 | Cite as

Global homeomorphisms and covering projections on metric spaces

Article

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.

Mathematics Subject Classification (1991)

58C15 58B20 46T05 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasUniversidad Autónoma del Estado de HidalgoPachucaMexico
  2. 2.Departamento de Análisis MatemáticoUniversidad Complutense de MadridMadridSpain

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