In the book *Open Problems in Topology* by Jan Van Mill and George M. Reed, the following problem was presented:
108. *Is there a para- Lindelof Dowker space?*
Recall that a *para-Lindelof Dowker space* has a locally countable open refinement, satisfies Axiom T4, and is not countably paracompact. 
Some results on this problem are in <http://topology.auburn.edu/tp/reprints/v11/tp11203.pdf>, where it is shown that the conditions are preserved under perfect mappings.
What is the status of this problem?
Any references are appreciated. 



Concerning Problem 108 in "Open Problems in Topology"
It is now problem 502 in "Open problems in topology II", I would guess it is still open.


