2.1 Facial structure
The notions of face, extreme point and exposed point of a convex set were defined in Section 1.4. In the present section we shall study the boundary structure of closed convex sets in relation to these and similar or more specialized notions. We shall assume in the following that is a nonempty closed convex set.
An i-dimensional face of K is referred to as an i-face. By we denote the set of all faces and by the set of all i-faces of K. A face of dimension dim K − 1 is usually called a facet. The empty ...