This is derived in Section 3 along $\langle$together$\rangle$ with a new proof of Morgan's theorem.
The proof proceeds along the same lines as the proof of Theorem 5, but the details are more complicated.
For direct constructions along more classical lines, see [KL].
Although these proofs run along similar lines, there are subtle adjustments necessary to fit the argument to each new situation.
Along the way, we come across some perhaps unexpected rigidity properties of familiar spaces.