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-   -   are the rational maps are Zariski-continuous? (http://mymathforum.com/abstract-algebra/35017-rational-maps-zariski-continuous.html)

tauasaf April 2nd, 2013 10:35 AM

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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