Universal Borel mappings and Borel actions of groups
type: Item
instance of: scholarly article
title: Universal Borel mappings and Borel actions of groups
zbMATH Open document ID: 1160.54024
published in: Topology and its Applications
publication date: 2008-11-12T00:00:00Z
review text: Let \(\mathbb D\) and \(\mathbb R\) be saturated classes of separable metrizable spaces. As examples of saturated classes, we point out the class of all separable metrizable spaces or the class of all separable metrizable spaces of locally finite dimension. Then the class of mappings of Borel class \(\alpha<\omega_1\) with domain in \(\mathbb D\) and range in \(\mathbb R\) contains a topologically universal mapping. Let \(G\) be a separable metrizable group. The class of all separable metrizable spaces \(X\in\mathbb D\) with actions of \(G\) of Borel class \(\alpha<\omega_1\) on them has a topologically universal element. Isometrical versions of the above results are also stated. All these results are improvements of former results of the author, where continuous mappings and actions were studied. The proofs use a construction of ``Containing Spaces'' from the author's book [Universal Spaces and Mappings, Noth-Holland Mathematics Studies, vol. 198, Elsevier (2005; Zbl 1072.54001)], where also the notion of saturated classes and several quoted results can be found.
reviewed by: Petr Holický
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 5365216
zbMATH Keywords: universal Borel mappings
zbMATH Keywords: universal Borel actions on groups
zbMATH Keywords: saturated classes
zbMATH Keywords: isometric universality
author: S. D. Iliadis
MaRDI profile type: Publication
full work available at URL: j.topol.2007.05.029
OpenAlex ID: W2077868152
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DOI: 10.1016/J.TOPOL.2007.05.029
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description: scientific article; zbMATH DE number 5365216