Let $A$ be an open ball in $\mathbb R^2$, show that $\mathbb R^2-A$ is connected.
I was assuming that $\mathbb R^2-A$ is disconnected, so that it has a separation. However, unlike how we prove $\mathbb R$ is connected (in which we assume $\mathbb R$ is disconnected and finding a point in $\mathbb R$ that does not belong to any part of the separation), I could not find such a point for $\mathbb R^2-A$. Can anyone give me some hint? Very much thanks!