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

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Bernal González, L. and Fernández Sánchez, j: and Seoane-Sepúlveda, Juan B. and Trutschnig, W. On special partitions of [0, 1] and lineability within families bounded variation functions. (Unpublished)

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Bounded variation function; Singular function; Absolutely continuous function; Nowhere monotonic function
Palabras clave (otros idiomas):Espacios vectoriales
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:73438
Deposited On:06 Jul 2022 08:08
Last Modified:06 Jul 2022 10:59

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