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Tagged with gn.general-topology p-adic-numbers
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Do algebraic completion/topological completion of fields always terminate? If so, are they unique?
Take the field $\mathbb{Q}$, If we complete it topologically with respect to the Euclidean norm, we get $\mathbb{R}$, then if we complete it algebraically, we get $\mathbb{C}$.
On the other hand, the ...
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