Covering properties in countable products
type: Item
instance of: scholarly article
title: Covering properties in countable products
zbMATH Open document ID: 0804.54009
author: Hidenori Tanaka
published in: Tsukuba Journal of Mathematics
publication date: 1994-06-19T00:00:00Z
review text: A space \(X\) is subparacompact (metacompact, respectively) provided that every open cover of \(X\) has a \(\sigma\)-discrete closed (point finite open, respectively) refinement. This paper studies conditions under which these and other covering properties are preserved by taking countable products. The key condition needed is a property called \({\mathcal D} {\mathcal C}\)-like, which is defined by using a topological game, and which involves closed sets that have discrete covers by compact subsets. Results in this paper include: a countable product of regular subparacompact (metacompact, respectively) \({\mathcal D} {\mathcal C}\)-like spaces is subparacompact (metacompact, respectively).
reviewed by: R. A. McCoy
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 91A44
zbMATH DE Number: 591465
zbMATH Keywords: countable products
zbMATH Keywords: topological game
MaRDI profile type: Publication
OpenAlex ID: W2107305528
DOI: 10.21099/TKBJM/1496162281
description: scientific article; zbMATH DE number 591465