On residual subsets of Darboux-Baire class 1 functions
type: Item
instance of: scholarly article
title: On residual subsets of Darboux-Baire class 1 functions
zbMATH Open document ID: 0572.26003
published in: Real Analysis Exchange
publication date: 1984-01-01T00:00:00Z
review text: The author considers the Banach spaces consisting of bounded Darboux- Baire one functions defined on [0,1], with the norm of the uniform convergence. There are the space of continuous functions, the space of bounded derivatives, Zahorski classes and others. He gives a table containing a list of 15 properties of functions, e.g.: The function is continuous almost everywhere. The function \(f(x)+rx\) is nowhere monotonic for every r. Each real number is a derived number of f(x) at each point. The table says whether the family of functions having a property is a residual subset of a space or not. Blanks in the table are for open problems.
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 3912665
zbMATH Keywords: Banach spaces
zbMATH Keywords: bounded Darboux-Baire one functions
zbMATH Keywords: norm of the uniform convergence
zbMATH Keywords: Zahorski classes
zbMATH Keywords: residual subset
author: Ibrahim H. I. Mustafa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3912665