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Deriving Dualities in Pointfree Topology from Priestley Duality
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Journal Article
Deriving Dualities in Pointfree Topology from Priestley Duality
2023
Overview
There are several prominent duality results in pointfree topology. 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.
Publisher
Springer Netherlands,Springer Nature B.V
