Hoover’s maximal limit spaces I: local strong sobriety, bounded sup-completeness and weak Hausdorffness

In 1995, Douglas Hoover introduced and studied a notion of maximal limit spaces: spaces in which every convergent net has a unique largest limit. This has connections with many other kinds of spaces that we have explored already, and I will show you one of Hoover’s theorems, suitably rephrased in light of a previous post of mine on weakly Hausdorff spaces (in the sense of Keimel and Lawson): the maximal limit spaces are exactly the locally strongly sober, bounded-sup-complete spaces, and therefore also the weakly Hausdorff, coherent, sober, bounded-sup-complete spaces. Read the full post.