Selections of the metric projection operator and strict solarity of sets with continuous metric projection

Abstract

In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained. Bibliography 25 titles.