On the (n,ℵ₀)-Lineability of Nowhere Differentiable Functions

2026/07/17 by Fábio Lima, Mônica Santos, Geivison Ribeiro
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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⊂ C[0,1] whose nonzero elements are nowhere differentiable can be extended to a countably infinite-dimensional subspace G⊂ C[0,1] with the same property.

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