Weakly Hausdorff spaces, and locally strongly sober spaces

A funny convergence of topics happened a few weeks ago. Frédéric Mynard told me about so-called locally strongly sober spaces (which, I am ashamed to say, I had heard about but completely forgotten about). At the same time, I was interested in so-called weakly Hausdorff spaces, as defined by Klaus Keimel and Jimmie Lawson in their paper on measure extension theorems for T₀ spaces. I realized that those two classes of spaces had a lot in common, and this led me to inquire whether that was a coincidence. As you may guess, this is not: we will see that the locally strongly sober spaces are exactly the weakly Hausdorff, coherent sober spaces. Read the full post.