Closure of the Right-Hand-Side Set for Systems of Nonlinear Inequalities

Consider the set of all vectors b such that the system g(x) ≦ b has a solution, where g: D → R^m, D ⊆ Rⁿ. This paper presents necessary and sufficient conditions for this set to be closed, with special results on continuous and convex functions, and gives an application to mathematical programming.