Internal descriptions of absolute Borel classes
type: Item
instance of: scholarly article
title: Internal descriptions of absolute Borel classes
zbMATH Open document ID: 1057.54026
author: Jan Pelant
author: Petr Holický
published in: Topology and its Applications
publication date: 2004-08-20T00:00:00Z
review text: For every topological space~\(X\) let \(\mathcal P(X)\) be a~class of subsets of \(X\). A Tikhonov space is an absolute \(\mathcal P\)-space if \(X\) is in \(\mathcal P(Y)\) whenever \(X\) is embedded in a Tikhonov space~\(Y\). In particular, if \(\mathcal P(X)\) is the class of Borel subsets of \(X\) we obtain the definition of an absolute Borel space. The authors consider the classes of certain natural hierarchies of Borel sets and scattered Borel sets and for these classes \(\mathcal P\) prove internal descriptions of absolute \(\mathcal P\)-spaces in terms of complete sequences of covers. They also briefly discuss the preservation of the obtained classes of spaces under open continuous maps and under perfect maps.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54D99
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 2093554
zbMATH Keywords: absolute Borel class
zbMATH Keywords: complete sequence of covers
zbMATH Keywords: open map
zbMATH Keywords: perfect map
MaRDI profile type: Publication
full work available at URL: j.topol.2003.10.004
OpenAlex ID: W2052942938
cites work: Q4853965
cites work: Q3994935
cites work: Q3976156
cites work: Q4281184
cites work: On the nonseparable theory of Borel and Souslin sets
cites work: On the non-separable theory of k-borel and k-souslin sets
cites work: Descriptive sets and the topology of nonseparable Banach spaces
cites work: Compact perfect sets in weak analytic spaces
cites work: Čech analytic and almost $K$-descriptive spaces
cites work: Luzin theorems for scattered-\(K\)-analytic spaces and Borel measures on them
cites work: Generalized Analytic Spaces, Completeness and Fragmentability
cites work: A generalization of functions of the first class
cites work: Q5541833
cites work: Absolute Borel sets and function spaces
cites work: A Note on Completely Metrizable Spaces
cites work: Partition-complete spaces are preserved by tri-quotient maps
cites work: On category-raising and dimension-raising open mappings with discrete fibers
cites work: On some class of Borel measurable maps and absolute Borel topological spaces
cites work: Borel \(\sigma\)-algebra on \([0,\Omega]\)
cites work: Choquet simplexes whose set of extreme points is K-analytic
cites work: Complete Exhaustive Sieves and Games
DOI: 10.1016/J.TOPOL.2003.10.004
description: scientific article; zbMATH DE number 2093554