Abstract
LetXbe a complete CAT(0)space with the geodesic extension property and Alexandrov curvature bounded below. It is shown that ifCis a closed subset ofX,then the set of points ofXwhich have a unique nearest point inCisGδand of the second Baire category inX.If, in addition,Cis bounded, then the set of points ofXwhich have a unique farthest point inCis dense inX.A proximity result for set-valued mappings is also included.
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