On dense-lineability of sets of functions on \(\mathbb R\)
type: Item
instance of: scholarly article
title: On dense-lineability of sets of functions on \(\mathbb R\)
zbMATH Open document ID: 1210.26008
author: David Pérez-García
author: J. B. Seoane-Sepúlveda
author: Richard M. Aron
author: Francisco García-Pacheco
published in: Topology
publication date: 2010-05-10T00:00:00Z
review text: A subset \(M\) of a topological vector space \(X\) is said to be dense lineable in \(X\) if there exists an infinite dimensional linear manifold in \(M \cup \{0\}\) which is dense in \(X\). Here, the authors obtain some interesting examples of function spaces on \(\mathbb{R}\) which are dense-lineable. In particular, they show that the set of differentiable nowhere monotone functions is dense-linable in \(\mathcal{C}[a, b]\).
reviewed by: Jafar Zafarani
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5706256
zbMATH Keywords: dense-lineability
zbMATH Keywords: differentiable nowhere monotone functions
MaRDI profile type: Publication
full work available at URL: j.top.2009.11.013
OpenAlex ID: W1970479850
Wikidata QID: Q59474359
DOI: 10.1016/J.TOP.2009.11.013
description: scientific article; zbMATH DE number 5706256