Quasi-relative interiors for graphs of convex set-valued mappings (Q828722)

The notion of the quasi-relative interior for convex sets is investigated in this work. New formulae, for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces, are obtained. The objective is to show how this notion plays a role in infinite dimensional spaces, in a manner that is analogous to the part played by the concept of relative interior, in finite-dimensional spaces.