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The algebraic closure of a \(p\)-adic number field is a complete topological field. (English) Zbl 1141.12002
Summary: The algebraic closure of a \(p\)-adic field is not a complete field with the \(p\)-adic topology. We define another field topology on this algebraic closure so that it is a complete field. This new topology is finer than the \(p\)-adic topology and is not provided by any absolute value. Our topological field is a complete, not locally bounded and not first countable field extension of the \(p\)-adic number field, which answers a question of Mutylin.
MSC:
12J99 Topological fields
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