will a nonempty countable and compact subset of a metric space always contain an isolated point? – math.stackexchange.com

will a nonempty countable and compact subset of a metric space always contain an isolated point? – math.stackexchange.com

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Let $(X,d)$ be a metric space, $K \subseteq X$ is nonempty, countable, and compact. I could not come up with an example where such a K has no isolated point(s). so I want to prove that an isolated ...

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