Geodesic
On Special Partitions of [0,1] and Lineability within Families of Bounded Variation Functions
Journal of convex analysis, Tome 30 (2023) no. 1, pp. 65-8
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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, 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 versions of already existing ones.
Classification : 15A03, 46B87, 26A45, 26B30
Mots-clés : Lineability, spaceability, bounded variation function, singular function, absolutely continuous function, nowhere monotonic function 
@article{JCA_2023_30_1_JCA_2023_30_1_a4,
     author = {L. Bernal-Gonz\'alez and J. Fern\'andez-S\'anchez and J. B. Seoane-Sepulveda and W. Trutschnig},
     title = {On {Special} {Partitions} of [0,1] and {Lineability} within {Families} of {Bounded} {Variation} {Functions}},
     journal = {Journal of convex analysis},
     pages = {65--8},
     year = {2023},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a4/}
}
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L. Bernal-González; J. Fernández-Sánchez; J. B. Seoane-Sepulveda; W. Trutschnig. On Special Partitions of [0,1] and Lineability within Families of Bounded Variation Functions. Journal of convex analysis, Tome 30 (2023) no. 1, pp. 65-8. http://geodesic.mathdoc.fr/item/JCA_2023_30_1_JCA_2023_30_1_a4/