Hausdorff and Box dimensions of continuous functions and lineability

DOI10.1080/03081087.2019.1612832zbMath1467.11075OpenAlexW2944491595MaRDI QIDQ5858680

Antonio Bonilla, Gustavo A. Muñoz-Fernández, José A. Prado-Bassas, Juan B. Seoane-Sepúlveda

Publication date: 14 April 2021

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://idus.us.es/handle//11441/86325

zbMATH Keywords

Hausdorff dimensionalgebrabilityspaceabilitylineabilityBox dimension

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Lineability, spaceability, and latticeability of subsets of \(C([0, 1)\) and Sobolev spaces] ⋮ Classical vs. non-Archimedean analysis: an approach via algebraic genericity

Cites Work

• Unnamed Item
• Unnamed Item
• On Weierstrass' monsters and lineability
• Peano curves on topological vector spaces
• The set of space-filling curves: topological and algebraic structure
• A simpler proof for the dimension of the graph of the classical Weierstrass function
• On dense-lineability of sets of functions on \(\mathbb R\)
• Hausdorff dimension of the graphs of the classical Weierstrass functions
• Basic sequences and spaceability in \(\ell_p\) spaces
• Dimension of the Graphs of the Weierstrass-Type Functions
• Linear subsets of nonlinear sets in topological vector spaces
• Lineability
• On the dimension of graphs of Weierstrass-type functions with rapidly growing frequencies
• On the Hausdorff Dimension of Some Graphs
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• Some results and open questions on spaceability in function spaces