Radial continuity of set-valued metric projections

AbstractSome new continuity concepts for metric projections are introduced which are simpler and more general than the usual upper and lower semicontinuity. These concepts are strong enough to generalize a number of known results yet weak enough so that now the converses of many of these generalizations are also valid. In particular, in a large class of normed linear spaces, suns and Chebychev sets can be characterized by a certain continuity property of their metric projections