First class selectors for upper semi-continuous multifunctions
type: Item
instance of: scholarly article
title: First class selectors for upper semi-continuous multifunctions
zbMATH Open document ID: 0644.54014
DOI: 10.1016/0022-1236(87)90102-9
author: R. W. Hansell
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: The paper improves selection theorems for arbitrary upper-semi-continuous multifunctions due to J. Jayne and C. A. Rogers. A concept of closed-end fragmentation of a Hausdorff space helps to find a sufficiently strong result to prove the existence of first Borel class selectors for multifunctions from a metric space X to (1) a metric space Y, or (2) the Banach space Y with its weak topology. Some strengthening for separable spaces and for \(c_ 0(\Gamma)\) is made. The selector is chosen to be a \(\sigma\)-discrete function from X to Y, and it is shown that some former results easily imply that such functions are in the first Baire class if Y is ``absolute extensor for metric spaces''. It is pointed out that the author's former proof of the stronger result, with Y being the extensor for X only, was not correct. The validity of this stronger claim remained unanswered.
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C50
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 4050523
zbMATH Keywords: Borel selector
zbMATH Keywords: upper-semi-continuous multifunctions
zbMATH Keywords: closed-end fragmentation
zbMATH Keywords: first Borel class selectors for multifunctions
zbMATH Keywords: \(\sigma \)- discrete function
zbMATH Keywords: absolute extensor
reviewed by: Petr Holický
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90102-9
OpenAlex ID: W2078145000
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description: scientific article; zbMATH DE number 4050523