Strongly proximinal subspaces of finite codimension in C(K)
We characterize strongly proximinal subspaces of finite codimension in C(K) spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in C(K) is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of C(K).