Generalizing witnesses to the non-normality of \(\mathbb N^{\omega_1}\)
For a closed set \(C\subset\mathbb N^{\omega_1}\) the following are equivalent: there is a countable closed discrete set \(D\) with \(C\) and \(D\) being disjoint but having no open separation; there is a closed set \(B\) which is disjoint from \(C\), is homeomorphic to \(C\) but has no open separation with \(C\); the frontier of \(C\) is non-Lindelöf. This generalises and extends Stone's counterexample to normality of \(\mathbb N^{\omega_1}\) as \(\{x\in\mathbb N^{\omega_1}\mid |x^{-1}(n)|\leq1 \forall n\not=0\}\) has non-Lindelöf boundary.
scientific article; zbMATH DE number 6137381