I have a question regarding the separative quotient featured in this question.
I want to show that for every dense subset D of the separative quotient Q it's preimage under h is also dense.
I have tried to fix an $x \in P$, find a $[y] \leq [x]$ and extract a $z \in [y]$ with $z \leq x$, but as as shown in the referenced topic this not always possible.
On the other hand since x and y are compatible I can find elements beneath x and y, but I don't see any way to make them part of $h^{-1}(D)$.
How do I use the premise more effectively or come up with possible counter-examples?