I'm currently reading a paper regarding lie groups, and the author says a few words about some set being Zarisky dense in $Aut(G)$ where G is a lie group, or $GL(V)$ where $V$ is a finite dimensional vector space, or some subspace of any of them (such as $Ad(H)$ for $H<G$ and $Ad$ the adjoint representation). This is essentialy the same anyways.
I've only encountered Zarisky topology on a vector space (or affine space), but not in the contest of a group such as $Aut(G)$ which isn't a vector space.
Any references/definitions would be great.
The determinant function from the vector (affine) space $M_n(K)\to k$ is a polynomial function. So $GL(V)$ or $GL(n)$ is the set-theoretic comlement of the Zariski closed set, defines by the condition det$\,=0$. Open set of Zariski topological space has the induced topology. That is what it is. Same way for closed sets also one can talk of Zariski topology.