On δ-normality

A subset G of a topological space is said to be a regular G_δ if it is the intersection of the closures of a countable collection of open sets each of which contains G. A space is δ-normal if any two disjoint closed sets, of which one is a regular G_δ, can be separated by disjoint open sets. Mack has shown that a space X is countably paracompact if and only if its product with the closed unit interval is δ-normal. Nyikos has asked whether δ-normal Moore spaces need be countably paracompact. We show that they need not. We also construct a δ-normal almost Dowker space and a δ-normal Moore space having twins.