On the $(n,\aleph_0)$-Lineability of Nowhere Differentiable Functions

Fábio Lima; Mônica Santos; Geivison Ribeiro

On the $(n,\aleph_0)$-Lineability of Nowhere Differentiable Functions

Functional Analysis 2026-07-17 v1

Authors: Fábio Lima , Mônica Santos , Geivison Ribeiro

Abstract

We establish a countable-dimensional extension property for the family of continuous nowhere differentiable functions, which we denote by $\ND[0,1]$ . More precisely, we prove that every finite-dimensional subspace $F\subset C[0,1]$ whose nonzero elements are nowhere differentiable can be extended to a countably infinite-dimensional subspace $G\subset C[0,1]$ with the same property.

Keywords

nowhere differentiable functions lineability countable-dimensional extension property Banach space

Cite

@article{arxiv.2607.15749,
  title  = {On the $(n,\aleph_0)$-Lineability of Nowhere Differentiable Functions},
  author = {Fábio Lima and Mônica Santos and Geivison Ribeiro},
  journal= {arXiv preprint arXiv:2607.15749},
  year   = {2026}
}