Stone Duality for Preordered Topological Spaces

A preordered topological space is a topological space with a preordering. We exhibit a Stone-like duality for preordered topological spaces, Inspired by a similar duality for bitopological spaces, due to Jung-Moshier and Jakl, and by a duality for preordered sets due to Bonsangue, Jacobs and Kok.