Skula spaces II: the Dow-Watson counterexample

Last time, we have started to explain some results due to A. Dow and S. Watson, and we have seen that every compact T₀ scattered space of scattering height at most 3 is Skula, namely can be obtained from a (necessarily Noetherian) space X by giving it its Skula topology instead. Today I will explain an example, also due to Dow and Watson, of a compact T₀ scattered space of scattering height 4 that is not Skula. Read the full post.