ABSTRACT
It is well known that the Lawson topology on an algebraic lattice is compact and zero dimensional. In fact, slightly more is true: an algebraic lattice A equipped with its natural order and Lawson topology is a compact, totally order-disconnected space; and, as such, is the dual space of a distributive lattice (isomorphic to the lattice of Lawson-clopen upper sets of A). We use the theory of continuous lattices to investigate the properties of distributive lattices arising in this fashion.
