On Single-Valuedness of Set-Valued Maps Satisfying Linear Inclusions.

1. Introduction and preliminaries Some basic notions of set-valued analysis, as linearity, affinity, convexity, additivity, are defined by linear inclusions (cf., e.g., [2]-[5], [8]-[12],[14]-[18]). Under appropriate conditions, such set-valued maps with the property that their value at a point is a singleton, are single-valued maps. We recall some known results of this type. Let X, Y be real vector spaces. We denote by [P.sub.0](Y) the collection of all nonempty subsets of Y. A set-valued map F : X [right arrow] [P.sub.0](Y) is called: