Open AccessProximinality in geodesic spaces
Author(s) -
Anchalee Kaewcharoen,
W. A. Kirk
Publication year - 2006
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/aaa/2006/43591
Subject(s) - algorithm , artificial intelligence , computer science
Let X be a complete CAT(0) space with the geodesicextension property and Alexandrov curvature bounded below. It is shown that ifC is a closed subset of X, then the set of points of X which have aunique 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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