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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spherically complete field ： ウィキペディア英語版 Spherically complete field In mathematics, a field ''K'' with an absolute value is called spherically complete if the intersection of every decreasing sequence of balls (in the sense of the metric induced by the absolute value) is nonempty: :$B\_1\backslash supseteq\; B\_2\backslash supseteq\; \backslash cdots\; \backslash Rightarrow\backslash bigcap\_\{n\backslash in\; \{\backslash mathbf\; N\}\}\; B\_n\backslash neq\; \backslash empty.$ The definition can be adapted also to a field ''K'' with a valuation ''v'' taking values in an arbitrary ordered abelian group: (''K'',''v'') is spherically complete if every collection of balls that is totally ordered by inclusion has a nonempty intersection. Spherically complete fields are important in nonarchimedean functional analysis, since many results analogous to theorems of classical functional analysis require the base field to be spherically complete. ==Examples== *Any locally compact field is spherically complete. This includes, in particular, the fields Q''p'' of completion of the algebraic closure of Q''p'', is not spherically complete. *Any field of Hahn series is spherically complete. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spherically complete field」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.