I have a map $f:\mathbb{R}^{4n} \rightarrow \mathbb{R}^{4n-4}: (x_1,\dots,x_n) \mapsto (x_1-x_2,\dots,x_{n-1} - x_n)$ and I need to know if it is a proper map. It has been ages since I had topology and I wouldn't even know how to begin.
Note that every $x_i \in \mathbb{R}^4$.