Let $f$ be an holomorphic function and $K(f)$ its non-escaping set (also called the filled Julia 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 ?