I learned in different math courses, that $\mathbb{C}$ is a clopen set. I'm very uncertain if I understand this right, please tell me if these two examples are true:
- $\mathbb{C} \setminus \{ 0 \}$ is open,
- $\mathbb{C} \setminus \{ z \in \mathbb{C} : |z| < 1 \}$ is closed.
Thanks.