I am trying to understand notations such as: $$\underset{x}{\min} \underset{y}{\max} f(x,y)$$
When we say $\underset{w}{\max} f(w)$, we mean the maximum value of $f$. When we say: $$\underset{y}{\max} f(x, y)$$
what do we mean? Does $\underset{y}{\max}$ returns a function of $x$ only?