Proximinality in geodesic spaces

Kaewcharoen, A.; Kirk, W. A.

doi:https://doi.org/10.1155/AAA/2006/43591

Abstract and Applied Analysis

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Volume 2006 | Article ID 043591 | https://doi.org/10.1155/AAA/2006/43591

Proximinality in geodesic spaces

A. Kaewcharoen¹and W. A. Kirk²

Received04 May 2006

Revised01 Aug 2006

Accepted10 Aug 2006

Published02 Nov 2006

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 Gδ 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.

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Copyright

Copyright © 2006 A. Kaewcharoen and W. A. Kirk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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