Khan - “The Irony in/of Economic Theory,” p. 780
⁶⁵: A set is convex if the line joining any two points chosen from the set also lies in the set. Thus a crescent is not a convex set whereas a disc is. See Rockafeller (1970) for details.
⁶⁶: This is nothing more profound than saying that one set lies on one side of the line and the other set lies on the other side of the line; see Rockafellar (1970) for details. Of course, with sufficient generality, the statement constitutes the geometric version of the fundamental Hahn-Banach theorem of functional analysis.