Priestley's duality for bounded distributive lattices has enjoyed growing attention and has been variously applied in the international literature since its inception in 1970. Whereas its introduction in [10] acknowledged the priority of Stone's 1937 treatment, claiming for itself only a "simpler" "more natural" "reformulation," the following fuller treatment [11] limited Stone to a non-referenced bibliographic item, as does the recently published book [4] which devotes several chapters to a detailed development of Priestley's duality.
In point of fact, the Stone and Priestley duals of a distributive lattice are the same space whose topology is described in formally different, but easily seen to be equivalent, ways: Any T 0 space with a distinguished base can be canonically re-equipped with a totally order disconnected topology simply by making the base clopen and retaining the T 0 partial order; in the other direction, the T 0 base can be recovered as the lattice of clopen increasing subsets of the compact dual. This coincidence of the duals is worked out by Cornish [3] (who also derives Priestley's duality from Stone's) in his preliminary lemmas, but who only draws the weaker conclusion that the two dual categories are isomorphic (which suffices for his purpose). This, and the inaccessibility of [3], may be responsible for these facts' lack of recognition.
The text which follows includes principally an exposition of the Stone duality theory and comprises the content of a series of three lectures in the algebra seminar at the University of Tennessee in Knoxville, given during the winter of 1992. I'm very grateful to the participants, especially to the two Davids and Michael S. Gilbert, for being such an alert and attentive audience.