L. Bernal-González

On Special Partitions of [0,1] and Lineability within Families of Bounded Variation Functions

We show that there exist large algebraic structures (vector spaces, algebras, closed subspaces, etc.) formed entirely (except for 0), on one hand, by singular, nowhere monotonic functions on [0,1] and, on the other hand, by absolutely continuous nowhere monotonic functions. Several tools, of independent interest, rel...