# Difficult simply connected problem

Suppose $\Omega$ is a bounded region. Let $L$ be a (two way infinite) line that intersects $\Omega$. Assume that $\Omega\cap L$ is an interval $I$. Choosing an orientation for $L$, we can define $\Omega_l$ and $\Omega_r$ to be subregions of $\Omega$ lying strictly to the left or right of L, with $\Omega=\Omega_l \cup I \cup \Omega_r$ a disjoint union. If $\Omega_l$ a $\Omega_r$nd are simply connected, then $\Omega$ is simply connected.