TITLE: Zariski topology over $\mathbb R$
QUESTION [6 upvotes]: What is a "Zariski topology on $\mathbb R$"? I don't think I quite understand the definition of a "Zariski topology". Thank you.

REPLY [5 votes]: Taking $\mathbb{R}$ as the affine line over reals, the Zariski topology of $\mathbb{R}$ consits of all its subsets whose complement is either finite or all of $\mathbb{R}$ (i.e. the finite complement topology.)