ON A LINDENBAUM COMPOSITION THEOREM

Abstract

We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [13] proved for real line, hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper \Delta^0_2-measurable functions.