Counterexamples

A few counterexamples in domain theory and in topology:

  1. A core-compact, non locally compact space
  2. Isbell’s non sober complete lattice
  3. Plotkin’s powerdomain and the hedgehog
  4. The Sorgenfrey line is not consonant
  5. Topological lattices and small semilattices (Lawson’s example of a topological lattice that does not have small semilattices)
  6. Compact scattered subspaces and a topological game (preparing for Costantini and Watson’s proof that Q is not consonant)
  7. The space S0
  8. On Till Plewe’s game and Matthew de Brecht’s non-consonance arguments
  9. Localic products and Till Plewe’s game
  10. Compact semilattices without small semilattices II: Gierz’s counterexample
  11. On products of dcpos, the Miao-Xi-Li-Zhao lemma, and the complete lattice Lfan (part I)
  12. The complete lattice Lfan (part II)
  13. When do products distribute over colimits in Top?

— Jean Goubault-Larrecq