  In this paper, we show that the Chvatal-Gomory closure of a compact convex
set is a rational polytope. This resolves an open question discussed in
Schrijver [Schrijver 80'] and generalizes the same result for the case of
rational polytopes [Schrijver 80'], rational ellipsoids [Dey-Vielma 10'] and
strictly convex sets [Dadush-Dey-Vielma 10']. In particular, it shows that the
CG closure of an irrational polytope is a rational polytope, which was the open
question in [Schrijver 80'].
