Set-theoretical entropies of Euler's totient function and other number theoretical special functions

In the following text we show set–theoretical entropy of Euler’s totient function and contravariant set–theoretical entropy of Dedekind psi function are zero. Also contravariant set–theoretical entropy of Euler’s totient function and set–theoretical entropy of Dedekind psi function are $+\mathrm{\infty }$. We pay attention to some of the other number theoretical special functions too. We continue our studies on Alexandroff topologies induced by Euler’s totient function and Dedekind psi function.