Strong c-algebrability of strong Sierpiński-Zygmund, smooth nowhere analytic and other sets of 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 Sierpiński-Zygmund, nowhere Hölder, Bruckner-Garg, nowhere monotone differentiable, a certain Baire class, smooth and nowhere analytic functions.

15 pages