Generalizing witnesses to the non-normality of \(\mathbb N^{\omega_1}\)
type: Item
instance of: scholarly article
title: Generalizing witnesses to the non-normality of \(\mathbb N^{\omega_1}\)
zbMATH Open document ID: 1267.54023
author: Keith M. Fox
published in: Topology and its Applications
publication date: 2013-02-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 6137381
zbMATH Keywords: non-normality
zbMATH Keywords: \(\mathbb N^{\omega_1}\)
zbMATH Keywords: countable closed discrete sets
zbMATH Keywords: non-Lindelöf
reviewed by: David B. Gauld
MaRDI profile type: Publication
full work available at URL: j.topol.2012.11.011
OpenAlex ID: W1977373329
DOI: 10.1016/J.TOPOL.2012.11.011
description: scientific article; zbMATH DE number 6137381