2026-06-01T01:26:40Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/652702025-04-08T14:47:42Zcom_20.500.14352_14col_20.500.14352_15
On special partitions of [0, 1] and lineability within families bounded variation functions
Bernal González, L.
Fernández Sánchez, j:
Seoane Sepúlveda, Juan Benigno
Trutschnig, W.
512.642
Lineability
Spaceability
Bounded variation function
Singular function
Absolutely continuous
function
Nowhere monotonic function
Espacios vectoriales
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
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.
Ministerio de Ciencia e Innovación (MICINN)
Junta de Andalucía
WISS 2025 project
Depto. de Análisis Matemático y Matemática Aplicada
Fac. de Ciencias Matemáticas
FALSE
unpub
2023-06-21T02:18:01Z
2023-06-21T02:18:01Z
journal article
https://hdl.handle.net/20.500.14352/65270
XXXX-XXXX
eng
PGC2018-098474-B-C21; PGC2018- 097286-B-I00
FQM-127 Grant P20-00637
open access
application/pdf