Let $X$ be a nowhere dense set of circle $S^1$. Here $S^1$ is equipped with the standard topology and measure.
Q Can we say that $X$ is a finite point set? Is there a counterexample?
2026-03-25 23:15:50.1774480550
nowhere dense set on circle
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Well, you can say it, but it would no be true. Just consider the set$$\left\{\left(\cos\left(\frac1n\right),\sin\left(\frac1n\right)\right)\,\middle|\,n\in\mathbb N\right\}\subset S^1.$$