The lattice generated by differentiable functions
type: Item
instance of: scholarly article
title: The lattice generated by differentiable functions
zbMATH Open document ID: 0641.26009
author: Tomasz Natkaniec
published in: Real Analysis Exchange
publication date: 1987-01-01T00:00:00Z
review text: Let \({\mathcal R}\) denote the family of all continuous functions \(f: R\to R\) such that (1) the set N(f) of all points at which f is not differentiable is a finite union of discrete sets; and (2) for every \(x\in R\) the right- hand derivatives \(f_+'(x)\) and the left-hand derivative \(f_-'(x)\) exist at x. In this article it is proven that \({\mathcal R}\) is the smallest lattice of functions containing all differentiable functions.
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 4044122
zbMATH Keywords: nondifferentiability
zbMATH Keywords: discrete sets
zbMATH Keywords: lattice of functions
zbMATH Keywords: differentiable functions
reviewed by: Zbigniew Grande
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4044122