  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 generalisations of relative
interior.
  We show that the face relative interior partitions convex sets into face
relative interiors of their closure-equivalent faces (different to the
partition generated by intrinsic cores), establish the conditions for
nonemptiness of this new notion, compare the face relative interior with other
concepts of convex interior and prove basic calculus rules.
