  A bijection $\psi$ is defined between the prime spectrum of quantum $SL_3$
and the Poisson prime spectrum of $SL_3$, and we verify that $\psi$ and
$\psi^{-1}$ both preserve inclusions of primes, i.e. that $\psi$ is in fact a
homeomorphism between these two spaces. This is accomplished by developing a
Poisson analogue of Brown and Goodearl's framework for describing the Zariski
topology of spectra of quantum algebras, and then verifying directly that in
the case of $SL_3$ these give rise to identical pictures on both the quantum
and Poisson sides. As part of this analysis, we study the Poisson primitive
spectrum of $\mathcal{O}(SL_3)$ and obtain explicit generating sets for all of
the Poisson primitive ideals.
