Minimax Results on Dense Sets and Dense Families of Functionals
研究了函数在定义域稠密子集上的下确界何时等于全局下确界，进而得到稠密集上的极小极大结果，并证明有界函数Banach空间中某些参数化泛函族的稠密性，给出James自反性定理的新证明。
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.