I've shown that every open set in the Zariski topology is open in the Euclidean topology, but I wonder why they are not equivalent. I'm searching for an open set in the Euclidean topology that is not open in Zariski.
2026-03-26 19:37:29.1774553849
Zariski and Euclidean topologies
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Hint: Consider the affine line $\mathbb{R}$, and let $U = \mathbb{R}\setminus \mathbb{Z}$.