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There is a theorem of Kurschák which asserts that the completion of a valued algebraically closed fied is algebraically closed. This is proved in Ribemboim's Paulo Ribenboim's The theory of classical valuations.

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There is a theorem of Kurschák which asserts that the completion of a valued algebraically closed fied is algebraically closed. This is proved in Ribemboim's The theory of classical valuations.