The authors study a class of subsets of \(R^ n\) that are “closed, convex and comprehensive”. Such a class arises in game theory and in production theory. The authors show that a “nice” subclass consisting of sets with smooth boundaries is “residual” in the original class. The authors transform the sets into epigraphs of convex functions and use the topology of epiconvergence studied by Attouch, Salinetti, Wets and others.