> [!NOTE] Definition (for subsets of $\mathbb{C}$) \[Analysis 3\] > A set $\Omega \subset C$ is connected if it cannot be expressed as the union of non-empty open sets $\Omega_1$ and $\Omega_2$ such that $\Omega_1 \cap \Omega_2=\varnothing$. An open, connected set $\Omega \subset \mathcal{C}$ is called simply connected if every closed curve in $\Omega$ can be continuously deformed to a point.