Prestreams and d-spaces

How do you model a topological space with a direction of time? That should seem easy; for example, a topological space with a preordering should be enough. But how do you model the directed circle, where times goes counterclockwise? That should seem harder. Fortunately, there are at least two satisfactory models: Marco Grandis’ d-spaces, and Sanjeevi Krishnan’s (pre)streams, which I will describe. Both appeared in 2009. Although they look rather different, they are connected by an idempotent adjunction, which restricts to an equivalence between so-called complete d-spaces and Haucourt streams, as discovered by Emmanuel Haucourt in 2012. Read the full post.