Lawson topology

Summary

The Lawson topology on a partially ordered set is the coarsest topology that contains both the Scott topology and the lower topology. The Scott topology sees only the "upward" behaviour of the order, so it is rarely Hausdorff. Adding the lower topology repairs this: on a continuous lattice the Lawson topology is compact and Hausdorff. It is the main tool for treating domains and continuous lattices as genuine compact spaces.