Only few results are known on continuity properties of the set-valued metric projection in nonlinear uniform approximation. In this paper we investigate this mapping in the case of best uniform approximation by splines of degree m with k free knots. A characterization of those functions at which the metric projection is upper semicontinuous is given. It follows that the metric projection is upper semicontinuous if and only if k ≤ m, and that it is upper semicontinuous at all "normal" functions. On the other hand, it is shown that the metric projection is never lower semicontinuous.
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