Stone duality for preordered topological spaces II. Ad-frames

A preordered topological space is a topological space X with a preordering ≤. I wish to explain a form of Stone duality for such preordered topological spaces. The idea is pretty simple: last time, we have seen a form of Stone duality for preordered sets, based on the premises that a preordered set is a topological space with an Alexandroff-discrete topology; hence a preordered topological space is a bitopological space, where one of the topologies is Alexandroff-discrete… and we have a Stone-like duality for bitopological spaces, Jung-Moshier duality, based on d-frames, a concept that we have seen in the June 2025 post. Read the full post.