Proximinality in geodesic spaces

A. Kaewcharoen and W. A. Kirk

Abstract and Applied Analysis, 2006, vol. 2006, 1-10

Abstract:

Let X be a complete CAT ( 0 ) space with the geodesic extension property and Alexandrov curvature bounded below. It is shown that if C is a closed subset of X , then the set of points of X which have a unique nearest point in C is G δ and of the second Baire category in X . If, in addition, C is bounded, then the set of points of X which have a unique farthest point in C is dense in X . A proximity result for set-valued mappings is also included.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:043591

DOI: 10.1155/AAA/2006/43591

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