The Hopf-Rinow Theorem in Infinite Dimension.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In this paper, the following theorem is proven. Let M be a complete, possibly infinite-dimensional, Riemannian manifold. Take any point q in M. Then the set of points p epsilon M which can be joined to q by a unique minimal geodesic contains a countable intersection of open dense subsets.
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