The structure of locally compact normal spaces: some quasi-perfect preimages
type: Item
instance of: scholarly article
title: The structure of locally compact normal spaces: some quasi-perfect preimages
zbMATH Open document ID: 1369.54013
published in: Topology and its Applications
publication date: 2017-05-02T00:00:00Z
review text: With \(W_0\subset\omega_1\) the set of isolated points and \(E\subset\omega_1\) any stationary, co-stationary subset containing \(W_0\), a locally compact, normal topology is constructed on \(X=W_0\cup[(E\setminus W_0)\times\mathfrak b]\) such that the projection \(\pi:X\to E\) is a quasi-perfect map. For each \(\alpha\in E\setminus W_0\), the fibre \(\pi^{-1}(\alpha)\) is homeomorphic to \(\mathfrak b\) with the usual topology and \(X\) is locally countable if and only if \(\mathfrak b=\omega_1\). The restriction \(W_0\subset E\) may be removed.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54D45
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E25
zbMATH DE Number: 6710339
zbMATH Keywords: locally compact
zbMATH Keywords: \(\omega_1\)-compact
zbMATH Keywords: countably compact
zbMATH Keywords: \(\sigma\)-countably compact
zbMATH Keywords: quasi-perfect map
author: Peter Nyikos
MaRDI profile type: Publication
full work available at URL: j.topol.2017.02.014
OpenAlex ID: W2593941062
cites work: Q3337413
cites work: A technique for constructing honest locally compact submetrizable examples
cites work: Q4523069
cites work: Q3327307
DOI: 10.1016/J.TOPOL.2017.02.014
description: scientific article; zbMATH DE number 6710339