Is it true that a morphism of affine algebraic varieties is continuous in Zariski topology? How should I proceed? thank you
Morphism of Affine Algebraic Variety
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algebraic-geometry
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1Hint: a function is continuous if and only if the pre-image of a closed set under the function is closed. So you should try to show that the pre-image of an algebraic variety is itself an algebraic variety, by finding an ideal that it is the variety of. – 2012-04-05
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0thank you for the reply.But need an explicit answer.it would be nice if you elaborate by an example. – 2012-04-05
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0That might be nice, but it would be *best* if you tried to use Matt's hint, and then told us where you get stuck. Why do you *need* an explicit answer? – 2012-04-05
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0@MimMim: have you tried thinking of one for yourself? – 2012-04-05
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2What's your definition of a morphism? – 2012-04-06
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0Dear Sir, My Definition of morphism is a polynomial map: $$\mathbb{A}^n\rightarrow \mathbb{A}^m$$ $$x\mapsto (F_1(x),\dots,F_m(x))$$ – 2012-04-06