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 $x \in X$,we consider the problem of finding a nearest point to $x$ in $A$. We define an appropriate complete metric space $\mathcal M$ of all pairs $(A,x)$ and construct a subset $Ω$ of $\mathcal M$ 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.