6. Spaces of prime and maximal ideals

For a lattice $L$, the prime ideal space $\Pi(L)$ is the set of all prime ideals of $L$, with a suitable topology. This is of special interest in the case where $L$ is Boolean, in which case $\Pi(L)$ is a Hausdorff space. However, $\Pi(L)$ is also of interest if $L$ is distributive. In both these cases the lattice can be recovered from the space.