On \(\delta\)-normality (Q1319413)

A space is said to be \(\delta\)-normal if any two disjoint closed sets of which one is a regular \(G_ \delta\) (the intersection of the closures of a countable collection of open sets containing this set) can be separated by open sets. Countably paracompact spaces are \(\delta\)-normal. The authors show that a space obtained from the space of countable ordinals by applying a modification due to G. M. Reed is a \(\delta\)- normal Moore space which is not countably paracompact. This space is then used to construct examples distinguishing between \(\delta\)-normality and some other generalizations of normality.