Some Minimax Results on Dense Sets and Dense Families of Functionals in C(K) and B(K)

In this paper, by an example we show that the general minimax results of Fan and Sion cannot be extended on usual dense sets. Nevertheless, we obtain some new minimax results on a special type of dense set that we call self-segment-dense. We apply our results in order to obtain denseness of some family of functionals in function spaces.