Independent Bernstein sets and algebraic constructions

DOI10.1016/j.jmaa.2012.03.007zbMath1253.26002OpenAlexW2095469803MaRDI QIDQ432350

Marek Bienias, Artur Bartoszewicz, Szymon Głąb

Publication date: 4 July 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.03.007

zbMATH Keywords

algebrabilitynowhere continuous compact to compact functionsnowhere continuous Darboux functionsperfectly everywhere surjective functionsstrongly everywhere surjective functions

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Banach spaces of continuous, differentiable or analytic functions (46E15) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (20)

Algebraic structures in the sets of surjective functions ⋮ Prescribed sets of continuity: Baire-Kuratowski theorem, derivatives, and lineability ⋮ The continuity properties of compact-preserving functions ⋮ Subsets of some families of real functions and their algebrability ⋮ Lineability, algebrability, and sequences of random variables ⋮ Large free linear algebras of real and complex functions ⋮ 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 ⋮ Lineability and algebrability within \(p\)-adic function spaces ⋮ Lineability, continuity, and antiderivatives in the non-Archimedean setting ⋮ Large function algebras with certain topological properties ⋮ Nonseparable spaceability and strong algebrability of sets of continuous singular functions ⋮ Algebraic genericity within the class of sup-measurable functions ⋮ Strong \(\mathfrak c\)-algebrability of strong Sierpiński-Zygmund, smooth nowhere analytic and other sets of functions ⋮ On lineability of families of non-measurable functions of two variable ⋮ Lineability of linearly sensitive functions ⋮ Classical vs. non-Archimedean analysis: an approach via algebraic genericity ⋮ Linear subsets of nonlinear sets in topological vector spaces

Cites Work

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• Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
• Independent Families in Complete Boolean Algebras
• Sierpiński-Zygmund functions and other problems on lineability
• A Characterization of Continuity Revisited
• Characterizing Continuity
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions
• Strong algebrability of sets of sequences and functions
• Algebrability of the set of non-convergent Fourier series

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