- Is $\mathbb{C}/\mathbb{Z}\cup\lbrace \pm i\infty\rbrace$ compact? Can we view it as a sphere?
- Is $(\mathbb{C}/\mathbb{Z}-\lbrace k/N\rbrace_{k=1}^{N})\cup \lbrace \pm i\infty\rbrace$ compact for some fixed $N\in \mathbb{N}$?
I'm confused with the second question since if we consider the space in 1. as a sphere, then we can view the space in 2. as sphere with several points taken out. Then using the subset topology, it seems like can make the space in 2. be compact.