Quasi-continuous domains and the Smyth powerdomain

“Quasi-continuous domains and the Smyth powerdomain” is the title of a very nice 2013 paper by Reinhold Heckmann and Klaus Keimel. I will not talk about quasi-continuous domains in this post. Rather, I will mention three pearls that this paper contains: one on so-called supercompact sets, a second one now called the topological Rudin Lemma, and finally a pretty surprising characterization of sober spaces that looks a lot like the definition of well-filteredness. Read the full post.