Geometry and topology of continuous best and near best approximations

The existence of a continuous best approximation or of near best approximat ions of a strictly convex space by a subset is shown to imply uniqueness of the best approximation under various assumptions on the approximating subs et. For more general spaces, when continuous best or near best approximatio ns exist, the set of best approximants to any given element is shown to sat isfy connectivity and radius constraints. (C) 2000 Academic Press.