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.