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Global homeomorphisms and covering projections on metric spaces

Gutú, Olivia and Jaramillo Aguado, Jesús Ángel (2007) Global homeomorphisms and covering projections on metric spaces. Mathematische Annalen, 338 (1). pp. 75-95. ISSN 0025-5831

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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.

Item Type:Article
Uncontrolled Keywords:Implicit Function Theorems; Manifolds; Mappings
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16611

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