Quantum $n$-space as a quotient of classical $n$-space

The prime and primitive spectra of $\mathcal{O}_{\mathbf q}(k^{n})$, the multiparameter quantized coordinate ring of affine $n$-space over an algebraically closed field $k$, are shown to be topological quotients of the corresponding classical spectra, $\operatorname{spec} \mathcal{O}(k^{n})$ and $\max \mathcal{O}(k^{n})\approx k^{n}$, provided the multiplicative group generated by the entries of $\mathbf{q}$ avoids $-1$.