Definition 1

Tag 00XF, permanent. Cite it as [Bourbaki, Tag 00XF].

Lie Groups and Lie Algebras, chapter VII, Appendix 1. Polynomial maps and Zariski topology

A polynomial map $f: V\rightarrow W$ is said to be dominant if the homomorphism from $A_W$ to $A_V$ associated to $f$ is injective.

In view of the preceding, $f$ is dominant if and only if $f(V)$ is dense in W in the Zariski topology.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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