Strong cc-algebrability of strong Sierpiński–Zygmund, smooth nowhere analytic and other sets of functions

We present a useful technique of proving strong cc-algebrability. As an outcome we obtain the strong cc-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.