FACE RELATIVE INTERIOR OF CONVEX SETS IN TOPOLOGICAL VECTOR SPACES

A new notion of face relative interior for convex sets in topological real vector spaces is introduced in this work. Face relative interior is grounded in the facial structure and may capture the geometry of convex sets in topological vector spaces better than other generalizations of relative interior. We show that the face relative interior partitions convex sets into face relative interiors of their closure-equivalent faces (different from the partition generated by intrinsic cores), establishes the conditions for nonemptiness of this new notion, compares the face relative interior with other concepts of convex interior, and proves basic calculus rules.