Function spaces in the Stegall class
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.
scientific article; zbMATH DE number 1682887