On functions that are almost continuous and perfectly everywhere surjective but not Jones. Lineability and additivity
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.
scientific article; zbMATH DE number 6836771
scientific article