Prove or disprove:
There is a metric space on $\mathbb{Q}$ such that this space be compact.
I find some examples of non equivalent metric on rational numbers, euclidean metric, p-adic and discrete metric but all of the them is not compact .
2026-04-07 22:57:53.1775602673
There is a metric space on $\mathbb{Q}$ such that this space be compact.
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Take a bijection between $\Bbb Q$ and the set $\{\frac{1}{n}\mid n\ge 1\}\cup \{0\}$ and use it to define the metric.