Confused about Algebraic Geometry Theorem

Let be a regular map between algebraic sets.

This induces a -algebra homomorphism given by

I have a theorem here that is really confusing me, and help would be appreciated.

It says " is injective is dense "

While proving this, the author takes density to mean . What has this got to do with density in the usual sense?

(where )

Re: Confused about Algebraic Geometry Theorem

Quote:

Originally Posted by

**slevvio** Let

be a regular map between algebraic sets.

This induces a

-algebra homomorphism

given by

I have a theorem here that is really confusing me, and help would be appreciated.

It says "

is injective

is dense "

While proving this, the author takes density to mean

. What has this got to do with density in the usual sense?

(where

)

Because is closed in the Zariski topology, and so being dense means the only closed set which contains it is the full space.

Re: Confused about Algebraic Geometry Theorem