Give an example of a closed pointset $\displaystyle F \subseteq \mathcal{N}$ and a continuous $\displaystyle f: \mathcal{N} \rightarrow \mathcal{N}$, such that the image $\displaystyle f[F]$ is not closed.

I can not seem to come up with a suitable example. I need help on this problem. In our book, pointsets are subsets of Baire space. Also, $\displaystyle \mathcal{N}$ denotes Baire space. Thanks in advance.