Continuous selections for the metric projection and alternation

AbstractIn this paper we give a characterization of those n-dimensional subspaces of C0(X), where X are certain locally compact spaces, for which alternation-elements are unique. As a consequence we obtain a result on the existence of continuous, quasi-linear selections for the metric projection in C0(X), which represents a partial solution of a problem posed by Lazar et al. [J. Functional Analysis 3 (1969), 193–216]. Furthermore, we establish a necessary condition for the existence of inner-radial-continuous selections for the metric projection in normed linear spaces. From this we deduce results on the nonexistence of inner-radial-continuous selections for the metric projection. Finally, we give a characterization of those exponential sums in C[a, b] which admit an inner-radial-continuous selection for their metric projection