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In the following text for a discrete finite nonempty set $K$ and a self-map $\varphi :X\to X$ we investigate interaction between different entropies of generalized shift ${\sigma }_{\varphi }:K^X\to K^X$, ${\left(x_{\alpha }\right)}_{\alpha \in X}\mapsto {\left(x_{\varphi \left(\alpha \right)}\right)}_{\alpha \in X}$ and cellularities of some Alexandroff topologies on $X$.