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April 2nd, 2013, 10:35 AM   #1
Joined: Mar 2013

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are the rational maps are Zariski-continuous?

How can one show that the a rational map f:V??W is Zariski-continuous? (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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