Exercise 14, § 5

Let A be a parabolic closed convex set (II, p. 67, exerc. 17) not containing a line. Show that if B is a closed convex set not meeting A then there exists a hyperplane in $\mathbf{R}^n$ that separates A strictly from B (if d is the Euclidean distance prove that $d(A, B) > 0$) ($cf.$ exerc. 12.)