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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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closed as too localized by algori, Gjergji Zaimi, Dan Petersen, J.C. Ottem, Leonid Positselski Sep 23 '11 at 9:29

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Can you give a simple description of the Zariski topology of a curve? – Hurkyl Sep 23 '11 at 1:40
Rather than create new tags "algebraic" and "geometry" I fixed the tagging – David White Sep 23 '11 at 2:51
I reverted the "faux-delete" that the OP attempted – Yemon Choi Mar 18 '13 at 8:21
up vote 19 down vote accepted

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.

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Hi. Welcome to MO. – Felipe Voloch Sep 23 '11 at 2:24

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