On typical bounded functions in the Zahorski classes
type: Item
instance of: scholarly article
title: On typical bounded functions in the Zahorski classes
zbMATH Open document ID: 0579.26003
author: Dan Rinne
published in: Real Analysis Exchange
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with real functions defined on the real interval [0,1]. Using the fact that the families \(bM_ i\) of bounded functions each of Zahorski's classes form a complete metric space under the sup norm, some typical results are given. E.g., it is proved that a typical function in each family \(bM_ i\) has every real number as a derived number at every point. The author also gives analogues of \textit{J. Ceder}'s and \textit{T. L. Pearson}'s results concerning \(bM_ 1\) [Acta Math. Acad. Sci. Hung. 37, 339-348 (1981; Zbl 0426.26003)] in each of the other Zahorski classes.
Mathematics Subject Classification ID: 26A21
zbMATH DE Number: 3927262
zbMATH Keywords: typical bounded Darboux Baire 1 function
zbMATH Keywords: complete metric space
zbMATH Keywords: Zahorski classes
reviewed by: Pavel Kostyrko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3927262