Algebrability of S-continuous functions

Considering the natural topology or S-density topology on the domain and on the range we obtain different families of continuous functions f:R→R. We prove that certain differences of those families are strongly c-algebrable, i.e., they contain c-generated free subalgebras. In particular, we obtain strengthenings of recent results of J. Hejduk, A. Loranty, R. Wiertelak, S. Lindner and M. Terepeta.