Special refinements and their applications on products
type: Item
instance of: scholarly article
title: Special refinements and their applications on products
zbMATH Open document ID: 0979.54010
DOI: 10.1016/S0166-8641(99)00016-4
author: Yukinobu Yajima
published in: Topology and its Applications
publication date: 2002-02-18T00:00:00Z
review text: The concept of a special refinement for the product of two spaces is introduced. The following are shown: (1) If \(X\) is \(HCP\)-netted and \(X \times Y\) is normal or countably paracompact, then every open cover of \(X \times Y\) has a special refinement. (2) If \(X\) is paracompact, \(Y\) is collectionwise normal (resp. collectionwise normal and countably paracompact), and every open cover (resp. every directed open cover) of \(X \times Y\) has a special refinement. Then a closed subset of \(X \times Y\) is \(P\)-embedded if and only if it is \(C\)-embedded. (3) Let \(X\) and \(Y\) be paracompact (resp. metacompact, subparacompact, submetacompact) spaces. If an open cover of \(X \times Y\) has a special refinement, then it has a \(\sigma\)-locally finite open refinement (resp. \(\sigma\)-point-finite open refinement, \(\sigma\)-locally finite closed refinement, \(\theta\)-sequence of open refinements).
reviewed by: Ken-ichi Tamano
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54E18
zbMATH DE Number: 1462706
zbMATH Keywords: product
zbMATH Keywords: open covering
zbMATH Keywords: special refinement
zbMATH Keywords: normal
zbMATH Keywords: countably paracompact
zbMATH Keywords: collectionwise normal
zbMATH Keywords: paracompact
zbMATH Keywords: metacompact
zbMATH Keywords: subparacompact
zbMATH Keywords: submetacompact
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1462706