Algebrability, non-linear properties, and special functions

TL;DR

This paper constructs large algebras within certain classes of special functions, advancing the understanding of their algebraic structures and properties.

Contribution

It introduces new uncountably generated algebras inside classes of Sierpiński-Zygmund, perfectly everywhere surjective, and nowhere continuous Darboux functions, improving previous results.

Findings

Constructed uncountably generated algebras in special function classes

Enhanced known results on algebraic structures of these functions

Demonstrated the richness of algebraic properties in pathological functions

Abstract

We construct uncountably generated algebras inside the following sets of special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere surjective functions and nowhere continuous Darboux functions. All conclusions obtained in this paper are improvements of some already known results.