9.6 Bifinite domains
A simple modification of the characterization of spectral spaces as projective limits of finite T0 spaces (i.e., finite posets) yields the so-called bifinite domains, a.k.a. Plotkin’s SFP-domains. Just like bc-domains, bifinite domains form one of the important categories used in domain theory (Abramsky and Jung, 1994). In particular, this category will turn out to be Cartesian-closed.
We require the maps rij : Aj → Ai to be retractions, and a bit more.
Definition 9.6.1 (ep-pair, projection) An ep-pair from a topological space X to a topological space Y is a pair of continuous maps such that r ○ s = idX and s ○ r idY. Then ...