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The statement is basically in the question. I know that $\mathbb{C}$ is algebraically closed and a complete metric space, which makes it a very interesting field. I was wondering if there were other fields which are algebraically closed and complete with respect to a metric. For instance, can this happen in characteristic $p$?

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    $\begingroup$ Another example $\endgroup$ – user553213 Apr 20 '18 at 0:15
  • $\begingroup$ thanks, do you know if this can happen in characteristic p? $\endgroup$ – Sheel Stueber Apr 20 '18 at 0:30

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