Stably locally compact locales are dual to continuous posets

Abstract

New localic characterisations are given of (i) stably locally compact locales and (ii) continuous posets . With the characterisations, these two separately studied classes of locales can be seen to be dual to one another. As an application we give outline proofs of de Groot and Hoffmann-Lawson duality, showing that the duality for both classes is essentially the same result.