On weak Chebyshev subspaces. II. Continuous selection for the metric projection and extension to Mairhuber's theorem

Abstract

The main result in this paper is the characterization of all n-dimensional weak Chebyshev Z subspaces of C( Q) for which the metric projection has a continuous selection. It is also shown that if n ⩾ 3 and P N has a continuous selection, then Q should be homeomorphic to a subset of R.