  There are several prominent duality results in pointfree topology. The
Hofmann-Lawson duality establishes that the category of continuous frames is
dually equivalent to the category of locally compact sober spaces. This
restricts to a dual equivalence between the categories of stably continuous
frames and stably locally compact spaces, which further restricts to Isbell
duality between the categories of compact regular frames and compact Hausdorff
spaces. We show how to derive these dualities from Priestley duality for
distributive lattices, thus shedding new light on these classic results.
