We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.

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 inX. If, in addition,C is bounded, then the set of points ofX which have a unique farthest point in C is dense in X. A proximity resu...

We show that in a Banach space X every closed convex subset is strongly proximinal if and only if the dual norm is strongly sub differentiable and for each norm one functional f in the dual space X∗, JX(f) the set of norm one elements in X where f attains its norm is compact. As a consequence, it is observed that if the dual norm is strongly sub differentiable then every closed convex subset of...