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.
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