Large free linear algebras of real and complex functions

DOI10.1016/j.laa.2013.01.013zbMath1337.15003arXiv1212.4329OpenAlexW2023071135MaRDI QIDQ1947130

Adam Paszkiewicz, Artur Bartoszewicz, Szymon Głąb

Publication date: 12 April 2013

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

Full work available at URL: https://arxiv.org/abs/1212.4329

zbMATH Keywords

algebrabilitystrong algebrabilitylineabilityperfectly everywhere surjective functionsstrongly everywhere surjective functionsset of continuity points

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (14)

Algebraic structures in the sets of surjective functions ⋮ Prescribed sets of continuity: Baire-Kuratowski theorem, derivatives, and lineability ⋮ Subsets of some families of real functions and their algebrability ⋮ Peano curves on topological vector spaces ⋮ On algebraic properties of the family of weakly Świątkowski functions ⋮ Additivity and lineability in vector spaces ⋮ Algebrability of some families of Darboux-like functions ⋮ Lineability, spaceability, and additivity cardinals for Darboux-like functions ⋮ Large free sets in powers of universal algebras ⋮ The set of space-filling curves: topological and algebraic structure ⋮ Large function algebras with certain topological properties ⋮ Strong \(\mathfrak c\)-algebrability of strong Sierpiński-Zygmund, smooth nowhere analytic and other sets of functions ⋮ Families of feebly continuous functions and their properties ⋮ Holomorphic surjectivity near the boundary: topological and algebraic genericity

Cites Work

• Unnamed Item
• Unnamed Item
• Independent Bernstein sets and algebraic constructions
• On algebrability of nonabsolutely convergent series
• Algebrability of conditionally convergent series with Cauchy product
• Lineability, spaceability, and algebrability of certain subsets of function spaces
• Lineability and algebrability of pathological phenomena in analysis
• Algebras in sets of queer functions
• An undecidable case of lineability in \(\mathbb R^{\mathbb R}\)
• Uncountably generated algebras of everywhere surjective functions
• Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
• Spaceability and algebrability of sets of nowhere integrable functions
• Independent Families in Complete Boolean Algebras
• Sierpiński-Zygmund functions and other problems on lineability
• A Characterization of Continuity Revisited
• Differentiation of Real Functions
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• Strong algebrability of sets of sequences and functions
• Algebrability of the set of non-convergent Fourier series

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