Unique continuous selections for metric projections of C(X) onto finite-dimensional vector subspaces, II

Best approximation in C(X) by elements of a Chebyshev subspace is governed by Haar's theorem, the de la Vallée Poussin estimates, the alternation theorem, the Remez algorithm, and Mairhuber's theorem. J. Blatter (1990, J. Approx. Theory 61, 194–221) considered best approximation in C(X) by elements of a subspace whose metric projection has a unique continuous selection and extended Haar's theorem and Mairhuber's theorem to this situation. In the present paper we so extend the de la Vallée Poussin estimates, the alternation theorem, and the Remez algorithm.