Countable metacompactness of products of LOTS'
type: Item
instance of: scholarly article
title: Countable metacompactness of products of LOTS'
zbMATH Open document ID: 1302.54065
author: Yasushi Hirata
author: Nobuyuki Kemoto
published in: Topology and its Applications
publication date: 2014-11-14T00:00:00Z
review text: A topological space \(X\) is said to be countably metacompact if each countable open cover has a point-finite open refinement. It is known that each LOTS and the product of two ordinals is hereditarily countably metacompact. For every regular uncountable cardinal \(\kappa,\) the authors construct a hereditarily paracompact LOTS \(L_\kappa\) such that \(L_\kappa\times S\) is not countably metacompact for any stationary set \(S\) in \(\kappa.\) They also find a condition on a GO-space \(X\) in order that \(X\times \kappa\) is countably metacompact. They conclude that a subspace \(X\) of an ordinal is paracompact if and only if \(X\times Y\) is countably metacompact for every GO-space \(Y.\)
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 03E10
zbMATH DE Number: 6369776
zbMATH Keywords: LOTS
zbMATH Keywords: countably metacompact
zbMATH Keywords: product space
zbMATH Keywords: subspace of an ordinal
zbMATH Keywords: stationary
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: j.topol.2014.08.010
OpenAlex ID: W1972180414
cites work: Q3994935
cites work: Paracompactness in ordered spaces
cites work: Products of monotonically normal spaces with various special factors
cites work: Q4326506
cites work: The product of two ordinals is hereditarily countably metacompact
cites work: Q5636033
DOI: 10.1016/J.TOPOL.2014.08.010
description: scientific article; zbMATH DE number 6369776