Normality and closed projections of products with a cardinal factor
type: Item
instance of: scholarly article
title: Normality and closed projections of products with a cardinal factor
zbMATH Open document ID: 0853.54012
DOI: 10.1016/0166-8641(95)00105-0
author: Nobuyuki Kemoto
author: T. Nogura
author: Yukinobu Yajima
published in: Topology and its Applications
publication date: 1997-01-09T00:00:00Z
review text: Let \(X\) be a normal space and let \(\kappa\) denote the space of ordinal numbers less than the initial ordinal of a regular cardinal \(\kappa\). The authors discuss the relationship between the following two conditions: (a) the product space \(X\times \kappa\) is normal; (b) the projection \(\pi_X: X\times \kappa\to X\) is a closed map. In particular, it is proved that if \(X\) is either \(<\kappa\)-paracompact and \(\kappa\)-compact or a \(<\kappa\)-paracompact GO-space, then (a) and (b) are equivalent. An example is given showing that there is a paracompact space \(X\) satisfying (a) but not (b).
reviewed by: Haruto Ohta
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D15
zbMATH DE Number: 896596
zbMATH Keywords: normal space
zbMATH Keywords: closed map
zbMATH Keywords: GO-space
zbMATH Keywords: paracompact space
MaRDI profile type: Publication
full work available at URL: 0166-8641(95)00105-0
OpenAlex ID: W1970827625
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description: scientific article; zbMATH DE number 896596