Limit of the complements of closed points.

Question

Given a scheme let's say $\mathbb{A}^n$ over a field $k$. The limit of all open subschemes is given by the spectrum of the function field i.e. $\text{Spec}(k(x_1,\ldots, x_n))$. Now consider the open subsets of $\mathbb{A}^n$ that are complements of a finite union of closed points (dimension zero closed subschemes). Does the limit of these open subschemes exit as a scheme? (transition maps are not affine) If so is it the same as $\text{Spec}(k(x_1,\ldots, x_n))$?