Characterizing global maximizers of the difference of sub-topical functions

For a certain class of elementary functions, which comprise a generalization of the class of min-type functions, we apply techniques from abstract convex analysis to obtain various characterizations of the maximal elements of the support sets of sub-topical functions. As an application, using this class of elementary functions, we characterize the global maximizers of the difference of two strictly sub-topical functions. These results have many applications in various areas of applied mathematics, mathematical economics, and game theory.