Global homeomorphisms and covering projections on metric spaces
Global homeomorphisms and covering projections on metric spaces
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全局同胚和度量空间上的覆盖投影
DOI：
10.1007/s00208-006-0068-9
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发表时间：
2006
影响因子：
1.4
通讯作者：
J. Jaramillo
中科院分区：
文献类型：
--
作者：
Olivia Gut'u;J. Jaramillo
对于一大类具有良好局部结构的度量空间，包括Banach-Finsler流形和上面有界的曲率测地空间，我们给出了局部同胚是覆盖投影的充分条件。我们首先得到一个关于路径连续性质的一般条件。作为结果，我们推导了涉及广义导数的路径提升的几个条件，特别地，我们得到了Hadamard整体逆定理在此背景下的推广。接下来，我们证明了在拟等距映射的情况下，这些充分条件中的一些也是必要的。最后，我们给出了整体隐函数存在性的一个应用。
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.