et
be a function
where the
and
are subsets of
and
respectively. We always
have
Therefore,
In this section we investigate the conditions for


(Minimax equality)

and attainment of the sup and inf.
Proposition
(Saddle point's defining property).
The pair
is a saddle point iff the relationship (
Minimax
equality
) holds and
We introduce the function
given
by


(definition of minmax p)

We will be using results of the section
(
Min common and max
crossing point section
). Following that section we define
