Algebrability of S-continuous functions

Abstract 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.