Localic Priestley duality
What is proved here is actually not a duality but a (covariant) equivalence: that between the localic analogues of the category of ordered Stone spaces (which were introduced by \textit{H. A. Priestley} in 1970 as the duals of distributive lattices) and of the category of coherent spaces (the non-Hausdorff generalization of Stone spaces which appeared in \textit{M. H. Stone}'s 1937 representation theorem for distributive lattices). The equivalence of these two categories (both being dual to the category of distributive lattices) has been well known for some time, even on the localic level; but this is the first entirely constructive proof of the result to appear in print.
scientific article; zbMATH DE number 1004388