# Zariski topology over $\mathbb R$

What is a "Zariski topology on $\mathbb R$"? I don't think I quite understand the definition of a "Zariski topology". Thank you.

-
Can you explain what exactly you don't understand in the definition of the Zariski topology in the case of $\mathbb R$? – Asaf Karagila Oct 10 '11 at 8:33

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.)