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