A Dowker space from a Lusin set
type: Item
instance of: scholarly article
title: A Dowker space from a Lusin set
zbMATH Open document ID: 0814.54001
DOI: 10.1016/0166-8641(94)90130-9
author: Paul J. Szeptycki
published in: Topology and its Applications
publication date: 1995-06-20T00:00:00Z
review text: A normal space is called a Dowker space if its product with the closed unit interval [0,1] is not normal. The author presents a construction of a first countable, locally countable Dowker space of size \(\aleph_ 1\) from a Luzin set. Let \({\mathcal A}\) be a Luzin subset of the real line. The topology \(\rho\) on \(\omega \times {\mathcal A}\) is defined such that (i) \((\omega \times {\mathcal A}, \rho)\) is normal, and (ii) \((\omega \times {\mathcal A},\rho)\) is not countably metacompact. The necessity of the assumption that \({\mathcal A}\) is a Luzin set is also denoted.
reviewed by: Akihiro Okuyama
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54G15
zbMATH DE Number: 612397
zbMATH Keywords: countably metacompact space
zbMATH Keywords: Dowker space
zbMATH Keywords: Luzin set
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90130-9
OpenAlex ID: W1986221675
cites work: A normal space X for which X×I is not normal
cites work: Q3681543
cites work: Partition Problems in Topology
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description: scientific article; zbMATH DE number 612397