On special partitions of [0, 1] and lineability within families bounded variation functions

Bernal González, L.Fernández Sánchez, j:Seoane Sepúlveda, Juan BenignoTrutschnig, W.2023-06-212023-06-21https://hdl.handle.net/20.500.14352/65270We 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.engOn special partitions of [0, 1] and lineability within families bounded variation functionsjournal articleopen access512.642LineabilitySpaceabilityBounded variation functionSingular functionAbsolutely continuous functionNowhere monotonic functionEspacios vectorialesMatemáticas (Matemáticas)Análisis matemático12 Matemáticas1202 Análisis y Análisis Funcional