Continuities of metric projection and geometric consequences (Q1369245)

This paper characterizes geometric structures (convexity, tabularity, and polyhedral structure) of a subset \(K\) of a normed linear space via different continuity conditions on the metric projection onto \(K\). In finite-dimensional spaces with the uniform norm, it is shown that convexity is equivalent to rotation-invariant almost convexity. Those sets every rotation of which have continuous metric projections are characterized.