Examples of functions on $\mathbb{R}$ which are continuous at a single point are well known. But what about $f:\mathbb{R}^2\to \mathbb{R}$ which is continuous at a single point? I tried to proceed as the one dimension case. I wanted to define $f=g\_1$ on $\mathbb{Q}\times \mathbb{Q}$ and $f=g\_2$ on $(\mathbb{R}\setminus \mathbb{Q})\times (\mathbb{R}\setminus \mathbb{Q})$ where $g\_1=g\_2$ has a unique solution. But in here I am leaving out $\mathbb{Q}\times (\mathbb{R}\setminus \mathbb{Q})$ and $(\mathbb{R}\setminus \mathbb{Q})\times \mathbb{Q}$. And I don't know what to define on those sets. Some ideas? I want to generalize such examples to $f :\mathbb{R}^n\to \mathbb{R}^m$. Thanks a lot.