Abstract: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 $\mathop{\sigma_\varphi:K^X\to K^X}$, ${(x_\alpha)_{\alpha\in X}\mapsto (x_{\varphi(\alpha)})_{\alpha\in X}}$ and cellularities of some Alexandroff topologies on $X$.
Keywords: Alexandroff topology; cellularity; functional Alexandroff topological space; infinite anti-orbit number; infinite orbit number
DOI: DOI 10.14712/1213-7243.2015.174
AMS Subject Classification: 54C70