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,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/43591 |
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| _version_ | 1832552461677625344 |
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| author | A. Kaewcharoen W. A. Kirk |
| author_facet | A. Kaewcharoen W. A. Kirk |
| author_sort | A. Kaewcharoen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ceab08b77e3040f39b65f32564fb1419 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ceab08b77e3040f39b65f32564fb14192025-02-03T05:58:37ZengWileyAbstract and Applied Analysis1085-33751687-04092006-01-01200610.1155/AAA/2006/4359143591Proximinality in geodesic spacesA. Kaewcharoen0W. A. Kirk1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USALet 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.http://dx.doi.org/10.1155/AAA/2006/43591 |
| spellingShingle | A. Kaewcharoen W. A. Kirk Proximinality in geodesic spaces Abstract and Applied Analysis |
| title | Proximinality in geodesic spaces |
| title_full | Proximinality in geodesic spaces |
| title_fullStr | Proximinality in geodesic spaces |
| title_full_unstemmed | Proximinality in geodesic spaces |
| title_short | Proximinality in geodesic spaces |
| title_sort | proximinality in geodesic spaces |
| url | http://dx.doi.org/10.1155/AAA/2006/43591 |
| work_keys_str_mv | AT akaewcharoen proximinalityingeodesicspaces AT wakirk proximinalityingeodesicspaces |