Closure, interior and boundary of $(0, 1)$ with Zariski topology If we consider $\mathbb{R}$ together with the Zariski topology, what is the closure, interior and boundary of $(0,1)$?
A set is closed iff it is either finite or $\mathbb{R}$ under this topology, so since the closure of $(0,1)$ must be closed am I right in thinking that this must be either $\{0,1\}$, $\emptyset$ or $\mathbb{R}$? I think if I can correctly understand the closure of this set I would be able to get the latter parts of my question.

The closure is the smallest closed superset, so in the case is $\Bbb R$. The interior is the greatest oper subset, so in this case is... And the border is...
