  The present paper deals with the perturbation analysis of set-valued
inclusion problems, a problem format whose relevance has recently emerged in
such contexts as robust and vector optimization as well as in vector
equilibrium theory. The set-valued inclusions here considered are parameterized
by variables belonging to a topological space, with and without constraints. By
proper techniques of variational analysis, some qualitative global implicit
function theorems are established, which ensure global solvability of these
problems and continuous dependence on the parameter of the related solutions.
Applications to parametric vector optimization are discussed, aimed at deriving
sufficient conditions for the existence of ideal efficient solutions that
depend continuously on the parameter perturbations.
