On dense-lineability of sets of functions on \(\mathbb R\) (Q968889)

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 \(\mathcal{C}[a, b]\).