Does $\mathbb Q_p$ have isolated points? I think that it doesn't,but i cannot prove it. Any help?Thank you!
2026-03-27 14:57:48.1774623468
Does the p-adic rationals have isolated points?
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Topologically, the $p$-adic integers, $\mathbb{Z}_p$ are all paths through a tree which splits $p$ times at every node, it is like a Cantor set, but based on $p$. So it is a perfect set with no isolated point. The $p$ adic rationals $\mathbb{Q}_p$ is a union of countabily many such trees, and so there will not be any isolated rationals either.