I have to show that the set $ A \subset C[0,1]$ defined by $A = [f \colon 0 \leq f(x) \leq 1 \forall x \in [0,1] ]$ is closed in the $||.||\_\infty$ norm.

Now i know the definition for open/closed set etc, but im not very good (or confident) in applying them. (especially when it comes to closed sets, open sets i find easier). How would i go about doing this?