Plotkin’s powerdomain and the hedgehog

There are three classical powerdomains in domain theory, named after Hoare, Smyth, and Plotkin. The first two are natural and well studied, and the third one is intricate and intriguing. To start with, there are several possible definitions for a Plotkin powerdomain, and while all of them are isomorphic in the nice cases of coherent continuous dcpo, or countably-based continuous dcpos, one may wonder whether they would coincide on all continuous dcpos. That is not the case, and I would like to present a funny counterexample, given in an exercise in Abramsky and Jung’s famous Domain Theory chapter. Let me also call it the hedgehog, because it has spines. Read the full post.