Function spaces in the Stegall class
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.54020
author: I. Kortezov
publication date: 2001-12-17T00:00:00Z
full work available at URL: https://eudml.org/doc/121590
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 1682887
zbMATH Keywords: spaces of continuous functions
zbMATH Keywords: set-valued mapping
zbMATH Keywords: Stegall class
zbMATH Keywords: minimal upper semicontinuous mapping
zbMATH Keywords: stability properties
MaRDI profile type: Publication
title: Function spaces in the Stegall class
published in: Commentationes Mathematicae Universitatis Carolinae
review text: A topological space \(X\) is of the Stegall class if every minimal upper semicontinuous mapping with non-empty compact values in \(X\) which is defined on a Baire space \(Z\) is single valued on a dense \(G_\delta \) subset of \(Z\). Metric spaces, and more generally spaces which are fragmented by a metric are of the Stegall class. The author investigates stability properties of the class of compact Hausdorff spaces \(T\) for which the space \(C(T)\) of continuous functions on \(T\) in the weak topology is of the Stegall class. He proves, for example, that this class is closed under products.
reviewed by: Eva Kopecká
description: scientific article; zbMATH DE number 1682887