Let B be a binary relation defined on the set of compact set…

Let B be a binary relation defined on the set of compact sets of Rn (the n-dimensional Euclidean space). That is, the alternatives offered to the agent are compact menus of elements from Rn. More precisely, let K={C:C is a compact set of Rn}. Then B is a binary relation on K. Suppose that B is represented by the function u(C)=min{f(x):x in C}, where f is a continuous function. Then,