On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity
type: Item
instance of: scholarly article
title: On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity
zbMATH Open document ID: 1384.26016
author: Tomasz Natkaniec
author: J. B. Seoane-Sepúlveda
author: Krzysztof Chris Ciesielski
author: José Luis Gámez-Merino
published in: Topology and its Applications
publication date: 2018-02-09T00:00:00Z
review text: The authors show that the class of functions that are perfectly everywhere surjective (PES) and almost continuous in the sense of Stallings (AC) but are not Jones functions (J) is \(\mathfrak{c}^+\)-lineable. This statement answers the following question: how ``large'' (in terms of algebraic genericity) is the class of functions in \(\mathbb{R}^{\mathbb{R}}\) that are perfectly everywhere surjective and almost continuous (in the sense of Stallings) but not Jones? Lower and upper bounds for the additivity of the class of functions \(\mathrm{PES} \cap \mathrm{AC} \setminus \mathrm{J}\) are also given. Finally, some open question are provided.
reviewed by: Zoltán Finta
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 6836771
zbMATH Keywords: lineability
zbMATH Keywords: additivity
zbMATH Keywords: perfectly everywhere surjective
zbMATH Keywords: Jones function
zbMATH Keywords: almost continuous function
zbMATH Keywords: Bernstein set
zbMATH Keywords: almost disjoint family
zbMATH Keywords: covering property axiom CPA
MaRDI profile type: Publication
full work available at URL: j.topol.2017.12.017
OpenAlex ID: W2772763945
cites work: Lineability
cites work: Powers of hypercyclic functions for some classical hypercyclic operators
cites work: On dense-lineability of sets of functions on \(\mathbb R\)
cites work: Lineability and spaceability of sets of functions on $\mathbb {R}$
cites work: Algebrability of the set of non-convergent Fourier series
cites work: Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
cites work: Additivity and lineability in vector spaces
cites work: Algebraic structures in the sets of surjective functions
cites work: Algebrability and nowhere Gevrey differentiability
cites work: Lineability criteria, with applications
cites work: Linear subsets of nonlinear sets in topological vector spaces
cites work: Basic sequences and spaceability in \(\ell_p\) spaces
cites work: Cardinal coefficients related to surjectivity, Darboux, and Sierpiński-Zygmund maps
cites work: Lineability, spaceability, and additivity cardinals for Darboux-like functions
cites work: Q4829656
cites work: Small Coverings with Smooth Functions under the Covering Property Axiom
cites work: Some results and open questions on spaceability in function spaces
cites work: A hierarchy in the family of real surjective functions
cites work: Large algebraic structures inside the set of surjective functions
cites work: Sierpiński-Zygmund functions and other problems on lineability
cites work: Lineability and additivity in \(\mathbb R^{\mathbb R}\)
cites work: An undecidable case of lineability in \(\mathbb R^{\mathbb R}\)
cites work: Sums and limits of almost continuous functions
cites work: Locally recurrent functions, density topologies and algebraic genericity
cites work: Almost continuity
cites work: Q4895350
DOI: 10.1016/J.TOPOL.2017.12.017
description: scientific article; zbMATH DE number 6836771