MINIMAX RESULTS ON DENSE SETS AND DENSE FAMILIES OF FUNCTIONALS

In this paper we deal with minimax results on dense sets. We first study under which conditions the infimum of a function over a dense subset of its domain coincides with the global infimum of that function. Then, we apply our results in order to obtain several minimax results on dense sets. Finally, we obtain the denseness of some parameterized families of functionals in the Banach space of bounded functions and we provide an alternative proof of the famous reflexivity result of James.