Convex hulls of integral points (Q1400866)

After reviewing some basic facts about convex sets and polyhedrons in \(\mathbb{R}^d\), the author studies convex hulls of lattice points \(x\in \mathbb{Z}^d\). He shows by an example that such a convex hull need not be closed. He then gives conditions on a set \(C\in \mathbb{R}^d\) which guarantee that the convex hull of \(C\cap \mathbb{Z}^d\) is closed and a generalized polyhedron (the latter means that any intersection with a polytope is a polytope). The conditions are in terms of the asymptotic cone of \(C\) and of the faces of \(C\).