Metric projections of closed subspaces of c0onto subspaces of finite codimension

Abstract

Let X be a closed subspace of c0. We show that the metric projection onto any proximinal subspace of nite codimension in X is Hausdor metric continuous, which, in particular, implies that it is both lower and upper Hausdor semicontinuous. 1. Proximinal subspaces of nite codimension. Let X be a real Banach space. Let D X and F be a map from D into a collection of non- empty subsets of X. If x2 D, the set-valued map F is lower semicontinuous at x if given > 0 and z in F (x), there exists > 0 such that for all y in D withkx yk 0, there exists > 0 such that F (y) F (x) +BX