Key points are not available for this paper at this time.
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category of ordered locales. The adjunction restricts to an equivalence of categories between spatial ordered locales and sober T0-ordered spaces with open cones.
Heunen et al. (2024) studied this question.