%0 Journal Article
%A Bernal González, L.
%A Fernández Sánchez, j:
%A Seoane-Sepúlveda, Juan B.
%A Trutschnig, W.
%T On special partitions of [0, 1] and lineability  within families bounded variation functions
%U https://hdl.handle.net/20.500.14352/65270
%X We show that there exists 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, related to obtaining special partitions of R into uncountable collections will be provided and used. The results obtained in this note are either new or improved version of already existing ones.
%~