Fubini properties for filter-related \(\sigma\)-ideals.
type: Item
instance of: scholarly article
title: Fubini properties for filter-related \(\sigma\)-ideals.
zbMATH Open document ID: 1047.54020
author: P. Zakrzewski
published in: Topology and its Applications
publication date: 2004-02-03T00:00:00Z
review text: It is shown that if \(\mathcal G, \mathcal F\subset [\omega]^{\omega}\) are two Borel filters with respect to the standard topology inherited from \(2^{\omega}\) and \(\mathcal F\) is a non-countably generated \(p\)-filter, then there is a set \(B\subset [\omega]^{\omega}\times [\omega]^{\omega}\), Borel in the standard topology, with ``vertical'' sections meager in the Ellentuck topology \(\tau_{\mathcal F}\) (generated by open sets \(\{X\in [\omega]^{\omega}:s\subset X\subset s\cup A\}\), \(s\in [\omega]^{<\omega}\), \(A\in\mathcal F\)) and complements of ``horizontal'' sections meager in \(\tau_{\mathcal G}\). Some finer results are given which give the same kind of example for \(\mathcal G\) with the Baire property and \(\mathcal F\) an arbitrary ultrafilter in \(\omega\). The above mentioned result would answer a question posed by Recław if the assumption on \(\mathcal F\) to be a \(p\)-filter could be omitted.
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 2037256
zbMATH Keywords: filter on \(\omega\)
zbMATH Keywords: meager sets
zbMATH Keywords: Ellentuck topology
zbMATH Keywords: Fubini property
reviewed by: Petr Holický
MaRDI profile type: Publication
full work available at URL: j.topol.2003.07.001
OpenAlex ID: W2015118492
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DOI: 10.1016/J.TOPOL.2003.07.001
description: scientific article; zbMATH DE number 2037256