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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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Official URL: http://www.springerlink.com/content/t2220x2731532124/fulltext.pdf
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Implicit Function Theorems; Manifolds; Mappings |
| Subjects: | Sciences > Mathematics > Algebraic geometry |
| ID Code: | 16611 |
| Deposited On: | 04 Oct 2012 08:53 |
| Last Modified: | 25 Jun 2018 07:29 |
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