Solution
= Solution
The closed interval does have the fixed-point property. If $f(x,0)=(F(x),0)$, then $F(0)-0\geq0$ and $F(1)-1\leq0$. The <intermediate value theorem> supplies $x\in[0,1]$ with $F(x)-x=0$.
= Solution
The closed interval does have the fixed-point property. If $f(x,0)=(F(x),0)$, then $F(0)-0\geq0$ and $F(1)-1\leq0$. The <intermediate value theorem> supplies $x\in[0,1]$ with $F(x)-x=0$.