Let S be a convex set in a linear space: 1. S and are faces of

Question:

Let S be a convex set in a linear space:
1. S and ∅ are faces of S.
2. The union of a collection of faces of S is a face.
3. The intersection of any nested collection of faces of S is a face.
4. The collection of all faces of S (partially ordered by inclusion) is a complete lattice.