arXiv subjects
Publications and source records attributed to S. Melzer.
We characterize Priestley spaces of algebraic, arithmetic, coherent, and Stone frames. As a corollary, we derive the well-known dual equivalences in pointfree topology involving various categories of algebraic frames.
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.
We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.