Ordered Locales

Abstract

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 $T_0$-ordered spaces with open cones.

23 pages, 5 figures; v2: added sections 7 and 8

References in corpus (1)

• A convenient category of locally preordered spaces