Why is the closure of $[-1,0)= \mathbb{R}$ in $\mathbb{R}$ with Zariski topology?
Why $[-1,0]$ is not considered as a closure? It is closed and it contains $[-1,0)$.
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Tim
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1Why not write down the definition of the Zariski topology, and then specialize to $\mathbb R$ ? – GEdgar Jul 26 '23 at 09:00
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Yes, I did so, the finite subsets of $\mathbb{R}$ and $\mathbb{R}$ itself are closed in the Zariski topology. In that case, wouldn't [-1,0] be closed? – Fazil Safarov Jul 28 '23 at 18:32
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I think $[-1,0]$ is not a finite set, nor is it $\mathbb R$. So it is not closed. – GEdgar Jul 28 '23 at 19:21