Cardinal coefficients related to surjectivity, Darboux, and Sierpiński-Zygmund maps

DOI10.1090/proc/13294zbMath1357.26005OpenAlexW2399842560MaRDI QIDQ3181314

L. Mazza, José Luis Gámez-Merino, Juan B. Seoane-Sepúlveda, Krzysztof Chris Ciesielski

Publication date: 29 December 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13294

zbMATH Keywords

additivityeverywhere surjective functionlineabilitycardinal coefficientsDarboux-likeSierpiński-Zygmund

Mathematics Subject Classification ID

Descriptive set theory (03E15) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Applications of set theory (03E75) Cardinal characteristics of the continuum (03E17)

Related Items

Algebraic structures in the sets of surjective functions ⋮ Lineability, spaceability, and latticeability of subsets of \(C([0, 1)\) and Sobolev spaces] ⋮ Lineability and additivity of almost injective functions ⋮ Self-similar functions, fractals and algebraic genericity ⋮ Lineability of the functions that are Sierpiński-Zygmund, Darboux, but not connectivity ⋮ Almost continuous Sierpiński-Zygmund functions under different set-theoretical assumptions ⋮ Algebraic genericity and the differentiability of the convolution ⋮ Algebras of measurable extendable functions of maximal cardinality ⋮ \( \mathfrak{c} \)-lineability: a general method and its application to Darboux-like maps ⋮ Maximal lineability of several subclasses of Darboux-like maps on \(\mathbb{R}\) ⋮ On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity ⋮ A hierarchy in the family of real surjective functions ⋮ Unnamed Item ⋮ Additivity coefficients for all classes in the algebra of Darboux-like maps on \(\mathbb{R}\) ⋮ Holomorphic surjectivity near the boundary: topological and algebraic genericity ⋮ A century of Sierpiński-Zygmund functions ⋮ Maximal lineability of the classes of functions in the algebra of Darboux-like maps that are Darboux but not connectivity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic structures in the sets of surjective functions
• Peano curves on topological vector spaces
• Large algebraic structures inside the set of surjective functions
• Almost continuity and connectivity - sometimes it's as easy to prove a stronger result
• Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions
• On dense-lineability of sets of functions on \(\mathbb R\)
• Lineability and additivity in \(\mathbb R^{\mathbb R}\)
• Almost continuity
• Algebraic properties of the class of Sierpiński-Zygmund functions
• Cardinal invariants concerning extendable and peripherally continuous functions
• Sierpiński-Zygmund functions that are Darboux, almost continuous, or have a perfect road
• Darboux-like functions within the classes of Baire one, Baire two, and additive functions
• Cardinal invariants concerning functions whose sum is almost continuous
• An undecidable case of lineability in \(\mathbb R^{\mathbb R}\)
• Uncountably generated algebras of everywhere surjective functions
• Algebrability and nowhere Gevrey differentiability
• Additivity and lineability in vector spaces
• Lineability, spaceability, and additivity cardinals for Darboux-like functions
• Lineability criteria, with applications
• Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
• Algebrability, non-linear properties, and special functions
• Linear subsets of nonlinear sets in topological vector spaces
• Lineability
• Sierpiński-Zygmund functions and other problems on lineability
• Set Theoretic Real Analysis
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• Some results and open questions on spaceability in function spaces
• Algebrability of the set of non-convergent Fourier series
• Zero-dimensional sets blocking connectivity functions