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

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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

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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.)

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Indeed, as follows from the simple observation that the set of zeroes of a polynomial is a finite set, and all finite sets can occur in this way. –  Henno Brandsma Oct 10 '11 at 19:09
    
@Henno Brandsma yes –  Dinesh Oct 11 '11 at 3:01

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