I doing a dynamic systems course and don't really know much topology yet, but the final work for the course requires me to prove for $\mathbb{T}^{2} = \{(x+m,y+n) : m,n \in \mathbb{Z}\} $ that the canonical projection $\pi: \mathbb{R}^{2} \rightarrow \mathbb{T}^{2}$ defined by $\pi (x,y) = \{(x+m,y+n) : m,n \in \mathbb{Z}\}$ is continuous.
I did some googling and found that in a product space all canonical projections are continuous, but I really have no idea on how to prove that since I'm not really familiar with this kind of thing at all. I couldn't really find anything else of use that I understood.
I'd greatly appreciate at least a hint on how to proceed, I've already mailed my professor but it'll take a while to get an answer and I'd like to get working on this as soon as possible.