Universally meager sets. II
type: Item
instance of: scholarly article
title: Universally meager sets. II
zbMATH Open document ID: 1141.03024
author: P. Zakrzewski
published in: Topology and its Applications
publication date: 2008-07-01T00:00:00Z
review text: Suppose that \(A\) is a subset of a perfect (that is, with no isolated points) Polish (that is, separable, completely metrizable) topological space \(X\). Then \(A\) is said to be universally meager if for every Borel isomorphism between \(X\) and the Cantor space \(2^\omega\) (or equivalently, a perfect Polish space \(Y\)) the image of \(A\) is meager. In this note, the author continues his study of universally meager sets, started in [Proc. Am. Math. Soc. 129, No. 6, 1793--1798 (2001; Zbl 0967.03043)], where it was proved that universally meager sets are a category analog of universally null sets. \textit{S. Todorcevic} [Adv. Math. 208, No. 1, 274--298 (2007; Zbl 1136.46013)] recently introduced another class of universally meager sets as follows: A subset \(A\) of a topological space \(X\) is universally meager in the sense of Todorcevic if for every Baire space \(Y\) and continuous nowhere constant map \(f: Y\to X\), the preimage \(f^{-1} (A)\) is meager in \(Y\). In this paper, the author discusses how these two classes are related.
reviewed by: T. Thrivikraman
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5295269
zbMATH Keywords: measure and category
zbMATH Keywords: Baire property
zbMATH Keywords: meager sets
zbMATH Keywords: Polish topology
MaRDI profile type: Publication
full work available at URL: j.topol.2008.05.005
OpenAlex ID: W2052526254
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DOI: 10.1016/J.TOPOL.2008.05.005
description: scientific article; zbMATH DE number 5295269