Paracompactness with respect to an ideal
type: Item
instance of: scholarly article
title: Paracompactness with respect to an ideal
zbMATH Open document ID: 0872.54014
DOI: 10.1155/S0161171297000598
author: T. R. Hamlett
author: Dragan Janković
author: David A. Rose
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1997-10-13T00:00:00Z
full work available at URL: https://eudml.org/doc/47709
review text: Summary: An ideal on a set \(X\) is a nonempty collection of subsets of \(X\) closed under the operations of subset and finite union. Given a topological space \(X\) and an ideal \({\mathcal I}\) of subsets of \(X\), \(X\) is defined to be \({\mathcal I}\)-paracompact if every open cover of the space admits a locally finite open refinement which is a cover for all of \(X\) except for a set in \({\mathcal I}\). Basic results are investigated, particularly with regard to the \({\mathcal I}\)-paracompactness of two associated topologies generated by sets of the form \(U-I\) where \(U\) is open and \(I\in {\mathcal I}\) and \(\bigcup \{U\mid U\) is open and \(U- A\in {\mathcal I}\), for some open set \(A\}\). Preservation of \({\mathcal I}\)-paracompactness by functions, subsets, and products is investigated. Important special cases of \({\mathcal I}\)-paracompact spaces are the usual paracompact spaces and the almost paracompact spaces of \textit{M. K. Singal} and \textit{S. P. Arya} [Math. Ann. 181, 119-133 (1969; Zbl 0162.26404)].
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54D30
zbMATH DE Number: 1054247
zbMATH Keywords: locally finite open refinement
zbMATH Keywords: almost paracompact spaces
MaRDI profile type: Publication
OpenAlex ID: W2080404440
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description: scientific article; zbMATH DE number 1054247