Let $f$ be a function, holomorphic in $\mathbb{C}$,  and $K(f)$ its non-escaping set : 
$$K(f) = \{ z \in \mathbb{C} : f^{(k)}(z)  \nrightarrow_{k \to \infty} \infty \} $$  

> **Question** : If $K(f)$ is connected, is it also contractible ?