Existence of pointwise-Lipschitz-continuous selections of the metric projection for a class of Z-spaces

AbstractWe study the problem of existence of pointwise-Lipschitz-continuous selections for the metric projection. We first approximate by finite dimensional subspaces of C(X) where X is a certain compact Hausdorff space and give a sufficient condition for existence of such selections. We apply this result to the case when X is the union of finitely many compact real intervals and get in this case a partial converse to a recent result of Brown