Friday, 7 May 2010

ag.algebraic geometry - Zariski open sets are dense in analytic topology

It is enough to show that the complement of U has empty interior. Also, that complement is contained in the zero set Z of a non-constant polynomial f, so it is enough to show that Z does not contain open sets.



If zinZ is a point in the interior of Z, then the Taylor series of f at z is of course zero. Since f is an entire function, this is absurd.

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