If we consider $\mathbb{A}^{1} \setminus \{0\}$ then we see this is isomorphic to $Z(xy-1) \subseteq \mathbb{A}^{2}$ via the map $g(t)=(t,\frac{1}{t})$. So this raises a question: let $n \geq 2$, is every proper open subset of $\mathbb{A}^{1}$, i.e a set of the form:
$\mathbb{A}^{1} \setminus \{c_{1},..,c_{n}\}$ isomorphic to a closed subset of $\mathbb{A}^{n+1}$? or $A^{k}$ for some $k \geq 2$?