Why are two curves over a field k homeomorphic?
I have been able to prove that any variety of positive dimension over a field k has the same cardinality as k.
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Alright I'll just answer so that I can get enough "reputation" to be able to comment and ask for a question to be closed because it belongs in other sites (see the faq).
A bijection between two topological spaces $f:X \rightarrow Y$ where open sets are complements of finite sets is a homeomorphism.