Algebrability of \(\mathcal{S}\)-continuous functions (Q2411483)

Four different families of continuous functions \(f : \mathbb{R} \to \mathbb{R}\) are introduced considering the natural topology or the \(\mathcal{S}\)-density topology on the domain and on the range. For certain differences of these families is proved that they are strongly \(\mathfrak{c}\)-algebrable (i.e. they contain \(\mathfrak{c}\)-generated free subalgebras).