Well-posedness and porosity in best approximation problems - Reich, Simeon; Zaslavski, Alexander J. (Topological Methods in Nonlinear Analysis, 2001)
Given a nonempty closed subset A of a Banach space X and a point x X, we consider the problem of finding a nearest point to x in A. We define an appropriate complete metric space M of all pairs (A,x) and construct a subset Ω of M which is the countable intersection of open everywhere dense sets such that for each pair in Ω this problem is well-posed. As a matter of fact, we show that the complement of Ω is not only of the first category, but also sigma-porous.