# Questions tagged [zariski-topology]

For questions about the topology of schemes and (classical) algebraic varieties.

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### If $f:\operatorname{Spec} A\to\operatorname{Spec} B$ is a map of schemes, how can I show $V(\varphi^{-1}(I)) = \overline{f(V(I))}$ for $I\subset B$?

If $X = \operatorname {Spec}(A)$ and $Y = \operatorname{Spec}(B)$ are affine schemes and I have a morphism $f : X \to Y$, then I am trying to show $$V(\varphi^{-1}(I)) = \overline{f(V(I))}$$ for any ...
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### Zariski density of a matrix semigroup generated by Jordan blocks

In the field of random matrix products, it seems a lot of theorems which give nice statistical properties (central limit theorem, large deviation, etc.) assume—among other things—a Zariski density ...
### affin line $\mathbb A_{R}^{1}$ is not homeomorphic to real line $\mathbb{R}$
I want to show affin line $\mathbb A_{R}^{1}$ is not homeomorphic to real line $\mathbb{R}$（the topology is euclidean topology）. I think the topology on $\mathbb A_{R}^{1}$ is just cofinite topology, ...