Every Hausdorff space is $T\_1$ and sober. Does the converse hold? I expect not. What's a counterexample?


I expected I should be able to look this up in *Counterexamples in Topology*, but unfortunately that book doesn't appear to discuss sober spaces.



Space which is $T_1$ and sober but not Hausdorff?
As Nate Eldredge points out in the comments, there's a counterexample on [Wikipedia](https://en.wikipedia.org/wiki/Sober_space). See there or Nate's comment for a description.


