Strong c-algebrability of strong Sierpi\'nski-Zygmund, smooth nowhere analytic and other sets of functions

TL;DR

This paper introduces a technique to prove strong -algebrability and applies it to demonstrate that various complex sets of functions, including Sierpiski-Zygmund and nowhere analytic functions, are strongly -algebrable.

Contribution

It develops a new method for establishing strong -algebrability and applies it to multiple classes of pathological functions.

Findings

Proves strong -algebrability of Sierpiski-Zygmund functions

Establishes strong -algebrability of nowhere Hf6lder and nowhere monotone differentiable functions

Shows strong -algebrability for functions in various Baire classes and smooth nowhere analytic functions

Abstract

We present a useful technique of proving strong $\mathfrak{c}$-algebrability. As an outcome we obtain the strong $\mathfrak{c}$-algebrability of the following sets of functions: strong Sierpi\'nski-Zygmund, nowhere H\"older, Bruckner-Garg, nowhere monotone differentiable, a certain Baire class, smooth and nowhere analytic functions.