Continuity and Lipschitz constants for projections (Q1044668)

Constructive proofs of some results from best approximation theory and properties of metric projections are given. For example, let \(Y\) be a locally compact subset of a complete metric space \(X\) such that each \(x \in X\) has a unique best approximation in \(Y\). Then the projection of \(X\) onto \(Y\) is sequentially continuous. Here, in order to prove sequential compactness of a complete totally bounded set, one needs to add the `limited principle of omniscience` (LPO) of intuitionistic logic.