Proximinality in geodesic spaces
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,...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/43591 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |