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April 2nd, 2013, 11:35 AM  #1 
Newbie Joined: Mar 2013 Posts: 2 Thanks: 0  are the rational maps are Zariskicontinuous?
How can one show that the a rational map f:V??W is Zariskicontinuous? (where V&W are affine varieties, i.e. irreducible closed algebraic sets) Interpret that, by definition we need to show that for every closed subset U?W f^(?1)(U):={P?dom(f):f(P)?U} is closed since U is closed there are polynomials h1,...,hn:W?k such that U={P?W:h1(P)= ... =hn(P)=0} and so we need to show that: f?1(U)={P?dom(f):h1?f(P)= ...= hn?f(P)=0} is closed, how can we show that? 

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