Global homeomorphisms and covering projections on metric spaces

• Autores: Olivia Gutú, Jesús Angel Jaramillo Aguado
• Localización: Mathematische Annalen, ISSN 0025-5831, Vol. 338, Nº. 1, 2007, págs. 75-95
• Idioma: inglés
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• Resumen

  • 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.