If we have some homeomorphism on $\bar{\mathbb{R}}=\mathbb{R}\cup\left\{\pm\infty\right\}$ this homeomorphism should have topological entropy Zero since $\bar{\mathbb{R}}$ is homeomorphic to $[0,1]$ and homeomorphisms on $[0,1]$ have Zero topological entropy. Am I right?
Is there something similar for homeomorphisms on $\bar{\mathbb{Z}}:=\mathbb{Z}\cup\left\{\pm\infty\right\}$?
Or maybe it is possible to say that a homeomorphism on $\bar{\mathbb{Z}}$ has Zero topological entropy since $\bar{\mathbb{Z}}\subset\bar{\mathbb{R}}$?