On the $(n,{\mathrm{\aleph }}_0)$-Lineability of Nowhere Differentiable Functions

We establish a countable-dimensional extension property for the family of continuous nowhere differentiable functions, which we denote by $\text{ND}[0,1]$. 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.