I got the definition of redundant like:
Let $X$ be a compact metric space and $T:X \rightarrow X$ a continuous map. Call a set $Y \subseteq X$ reundant for $T$ if $T(Y) \subseteq T(X \setminus Y)$.
Now I have to prove, that if $T$ has a redundant nonempty open set, then $T$ cannot be minimal. Is the converse true?
I think the converse is not true, for example the identity function on $[0,1]$ is a counterexample right?