Open Problems

This is a list of questions that I have not managed to solve yet, or that I think should be left to others.  If you have any solution, total or partial, please contact me at goubault (at)

I am looking for brilliant students in the field.  Finding a solution to one of those problems may convince me that I should hire you!

I’ll update that list from time to time, adding new problems, removing solved problems, and so on. I am not offering any guarantee that this will change often!

  1. Ordinal heights of Noetherian spaces (difficulty: moderate; suitable for a good M2 or PhD student; posted 23 feb 2017)
  2. FAC spaces (difficulty: pretty hard; suitable for an excellent PhD student; posted 23 feb 2017; solved 30 oct 2017, not that hard after all)
  3. Topologies on spaces of Lipschitz Yoneda-continuous maps (difficulty: really tough; posted 23 feb 2017)
  4. Full abstraction for languages with demonic and probabilistic choice (difficulty: moderate; suitable for a good M2 or PhD student; posted 08 nov 2017; can be considered solved, somehow; posted 4 feb 2019 [with some delay, sorry])
  5. Gδ subspaces of locally compact sober spaces (difficulty: high; posted 30 mar 2018).
  6. Core-compact vs. locally compact, well-filtered vs. sober (difficulty: high; posted 5 fev 2019).   Most—not quite all—of the open problems on that subpage have been solved now (July-September 2019).
  7. Statures and dimensions of spaces of trees, of infinite words (difficulty: high; posted 20 dec 2021).

Jean Goubault-Larrecqjgl-2011