It's the discrete topology. I have to proof that if I have $(X,\tau)$ and $(Y,\delta)$ two topological spaces, if every function $f:X\longrightarrow Y$ is continuos then $\tau$ is the discrete topology. I don't know what is the way to solve this. Thanks!

You need $\delta$ to be a non-trivial topology. So there must be an open set $U\in\delta$ such that $U\neq \emptyset$ and $U\neq Y$.
Then select $y_1\in U$ and $y_2\notin U$, and for $B\subseteq X$ define $f_B(x)=y_1$ if $x\in B$ and $f_B(x)=y_2$ if $x\notin B$. Then $f_B$ is continous, so $f_B^{-1}(U)=B$ must be open in $\tau$. 
