Productive Lindelöfness and a class of spaces considered by Z. Frolík
type: Item
instance of: scholarly article
title: Productive Lindelöfness and a class of spaces considered by Z. Frolík
zbMATH Open document ID: 1252.54006
published in: Topology and its Applications
publication date: 2012-08-16T00:00:00Z
review text: A topological space \(X\) is productively Lindelöf if \ \(X\times Y\) \ is Lindelöf for every Lindelöf space \(Y\). Among many other interesting results the authors prove that closed subspaces of countable products of \(\sigma\)-compact spaces are productively Lindelöf if and only if there are no Michael spaces \ (a Michael space is a Lindelöf space \(X\) whose product with the space of irrationals is not Lindelöf). In addition the authors prove that, assuming \(CH\), if \(X\) is productively Lindelöf and the union of \(\aleph_1\) compact sets, then \(X^{\omega}\) is Lindelöf.
reviewed by: Maximilian Ganster
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54D45
Mathematics Subject Classification ID: 54G20
Mathematics Subject Classification ID: 03E50
zbMATH DE Number: 6066693
zbMATH Keywords: Alster
zbMATH Keywords: Michael space
zbMATH Keywords: productively Lindelöf
zbMATH Keywords: Rothberger
zbMATH Keywords: \(\sigma\)-compact
MaRDI profile type: Publication
full work available at URL: j.topol.2012.05.022
OpenAlex ID: W1996974135
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DOI: 10.1016/J.TOPOL.2012.05.022
author: Peter Burton
author: Franklin D. Tall
description: scientific article; zbMATH DE number 6066693