Intersection of a closed convex set and an affine set

Question

Is the intersection of a closed convex set of $\mathbb{R^n}$ and an affine set $\mathbb{R^k} \subset \mathbb{R^n}, k \le n$ a closed convex set of $\mathbb{R^n}$? (closed convex sets are convex sets that contain all their limit points.)

Answer 1

Yes, because affine subspaces are closed and convex, and the intersection of (any finite family family of) closed, convex sets is closed and convex (essentially by definition).