Extending Baire-one functions on topological spaces
type: Item
instance of: scholarly article
title: Extending Baire-one functions on topological spaces
zbMATH Open document ID: 1075.54011
published in: Topology and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The paper consists of six sections: Introduction, Preliminaries, Extension of Baire-one functions, Counterexamples and questions, Extension of mappings of the first Borel class, Extension of Baire-one functions on compact convex sets. In the introduction the authors describe the history of the problem, the main result and give the summary of two last sections. Section 2 contains necessary definitions and propositions. In Section 3 the authors prove their main result on extending Baire-one functions (Theorem 13): Let \(Y\) be a Lindelöf hereditarily Baire subset of a completely regular space \(X\) and \(f\) be a Baire-one function on \(Y\). Then there exists a Baire-one function \(g\) on \(X\) such that \(f=g\) on \(Y\), \(\inf (f(Y)_=\inf (g(X))\), \(\sup (f(Y))=\sup(g(X))\). In Section 4 the authors collect several examples showing that the assumptions of their main theorem cannot be weakened in a natural way. They also collect here some open questions. In Section 5 the authors show that once it is possible to extend Baire-one functions, the extension theorem can be obtained even for \(F_\sigma\)-measurable mappings with values in Polish spaces. The last section of the paper is devoted to an application in convex analysis (which motivated the authors research).
reviewed by: Aleksandr A. Ivanov
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 2173004
zbMATH Keywords: Baire-one function
zbMATH Keywords: Lindelöf (hereditarily Baire
zbMATH Keywords: Michael) space
zbMATH Keywords: extension
zbMATH Keywords: compact convex set.
author: Ondřej F. K. Kalenda
author: J. Spurný
MaRDI profile type: Publication
full work available at URL: j.topol.2004.09.007
OpenAlex ID: W2038294302
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DOI: 10.1016/J.TOPOL.2004.09.007
description: scientific article; zbMATH DE number 2173004