Perfect images of absolute Souslin and absolute Borel Tychonoff spaces
type: Item
instance of: scholarly article
title: Perfect images of absolute Souslin and absolute Borel Tychonoff spaces
zbMATH Open document ID: 1028.54034
DOI: 10.1016/S0166-8641(02)00356-5
author: J. Spurný
author: Petr Holický
published in: Topology and its Applications
publication date: 2003-07-29T00:00:00Z
review text: One of the main results of the paper says that perfect images of Tychonoff scattered-\(K\)-analytic spaces are scattered-\(K\)-analytic if they are Tychonoff. This answers a question of \textit{R.~W. Hansell} [Serdica Math.~J.~27, 1-66 (2001; Zbl 0982.46012)] who introduced scattered-\(K\)-analytic spaces in the context of nonseparable Banach spaces. At the same time the authors get an alternative simple proof of the result of R.~W. Hansel and S.~Pan saying that Čech-analytic spaces are preserved by perfect mappings. The authors also generalize a~result of J.~Saint-Raymond and a~result of J.~E. Jayne and C.~A. Rogers on stability of various absolute Borel classes with respect to perfect mappings to the nonmetrizable case. In fact, more general absolute descriptive classes and their stability with respect to perfect mappings are investigated.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 1955999
zbMATH Keywords: perfect mapping
zbMATH Keywords: Souslin operation
zbMATH Keywords: Borel sets
zbMATH Keywords: analytic spaces
zbMATH Keywords: perfect images
MaRDI profile type: Publication
cites work: Q3884816
cites work: Q3994935
cites work: Q5725244
cites work: Q4281184
cites work: Descriptive sets and the topology of nonseparable Banach spaces
cites work: General Embedding Properties of Absolute Borel and Souslin Spaces
cites work: Perfect Images of Cech-Analytic Spaces
cites work: Čech analytic and almost $K$-descriptive spaces
cites work: Generalized Analytic Spaces, Completeness and Fragmentability
cites work: Topological Properties of Banach Spaces
cites work: Q3954510
cites work: A generalization of functions of the first class
cites work: Q5541833
cites work: Radon‐Nikodým compact spaces and fragmentability
cites work: On some class of Borel measurable maps and absolute Borel topological spaces
cites work: K ‐analytic sets
cites work: Absolute F σ Spaces
cites work: Q4104547
cites work: Embedding metric absolute Borel sets in completely regular spaces
full work available at URL: s0166-8641(02)00356-5
OpenAlex ID: W2024787273
description: scientific article; zbMATH DE number 1955999