I've found very nice problem in math analysis book but I can't solve it:
We define $c$ function as $c : \mathbb{I^2} \rightarrow \mathbb{R}$ and $\mathbb{I^2}$ means closed square in $\mathbb{R^2}$ with vertices $( \pm 1, \pm 1)$.
Is it true that continuous function $c$ can be injective?
How can I solve this problem?