Generalizing witnesses to the non-normality of [formula omitted

Abstract

We generalize A.H. Stoneʼs witnesses to the non-normality of Nω1 and produce new strong witnesses to the non-normality with a pair of disjoint countable closed discrete sets that fail to have an open separation by open sets having disjoint closures. Our generalization of A.H. Stoneʼs witnesses yields among other things that all closed subsets of Nω1 with non-Lindelöf boundaries fail to have an open separation with a closed disjoint homeomorphic copy of themselves.