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)

Jean Goubault-Larrecq