Reading this post here Problem in proving that $\mathbb{A}^2$ is not homeomorphic to $\mathbb{P}^2$
I came up with the following question:
Why are the $\mathbb A^1$ and $\mathbb P ^1 $ homeomorphic? (with the Zariski topology endowed, and algebraically closed underlying field)
Sorry, if this is something very easy, but I can't understand it.
Any help would be really appreciated!
Since an algebraically closed field is necessarily infinite, $\mathbb{A}^1$ and $\mathbb{P}^1$ have the same cardinality, and on both the Zariski topology is the cofinite topology. Therefore they are homeomorphic.