Exercise 19, § 2

a) Let A be an unbounded closed convex set in $\mathbf{R}^n$, that does not contain any line, but does contain an interior point. Show that the frontier of A is homeomorphic to $\mathbf{R}^{n-1}$ (use exercs. 15, b) and 18). b) In a Hausdorff topological vector space E, let A be a closed convex set that does not contain any line and is of dimension $\geq 2$. Show that the frontier of A is connected (use a) and GT, VI, § 2, exerc. 12).