Abstract and Applied Analysis
Volume 2006 (2006), Article ID 43591, 10 pages
Proximinality in geodesic spaces
1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Department of Mathematics, University of Iowa, Iowa City 52242-1419, IA, USA
Received 4 May 2006; Revised 1 August 2006; Accepted 10 August 2006
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.
Let be a complete CAT space with the geodesic
extension property and Alexandrov curvature bounded below. It is shown that if
is a closed subset of then the set of points of which have a
unique nearest point in is and of the second Baire category in If, in addition, is bounded, then the set of points of which have a unique farthest point in is dense in A proximity result for set-valued mappings is also included.