Typical continuous functions are not iterates
type: Item
instance of: scholarly article
title: Typical continuous functions are not iterates
zbMATH Open document ID: 0709.26001
DOI: 10.1007/BF01951395
published in: Acta Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: The author proves that the set \(\{f\in C^ 1_ 0:\) \(f=\phi^ k\), \(\phi \in C^ 1_ 0\), \(k\geq 2\}\) is of the first category in \(C^ 1_ 0\), where \(C^ 1_ 0\) denotes the set of continuous functions mapping [0,1] into itself.
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 4165198
zbMATH Keywords: typical continuous functions
zbMATH Keywords: first category set
zbMATH Keywords: set of continuous functions
author: Károly Simon
reviewed by: Ryszard Pawlak
MaRDI profile type: Publication
cites work: Differentiation of real functions
cites work: A historical note on the measurability properties of symmetrically continuous and symmetrically differentiable functions
description: scientific article; zbMATH DE number 4165198