  In this paper, we provide an equivalent condition for the Chvatal-Gomory (CG)
closure of a closed convex set to be finitely-generated. Using this result, we
are able to prove that, for any closed convex set that can be written as the
Minkowski sum of a compact convex set and a closed convex cone, its CG closure
is a rational polyhedron if and only if its recession cone is a rational
polyhedral cone. As a consequence, this generalizes and unifies all the
currently known results, for the case of rational polyhedron and compact convex
set.
