I need to show that $X=\{f\in[0,1]^{[0,1]}:\forall a,b\in[0,1](a<b\Rightarrow f(a)\leq f(b))\}$ with the pointwise convergence is compact.
For that I'm trying to show that $[0,1]^{[0,1]}$ is itself compact, because I can easily show that $X$ is closed in this space; and, therefore, compact. But I'm failing to show that as well.