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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 neighbourhood system ： ウィキペディア英語版 neighbourhood system In topology and related areas of mathematics, the neighbourhood system, complete system of neighborhoods, or neighbourhood filter $\backslash mathcal(x)$ for a point ''x'' is the collection of all neighbourhoods for the point ''x''. == Basis == A neighbourhood basis or local basis for a point ''x'' is a filter base of the neighbourhood filter, i.e. a subset :$\backslash mathcal(x)\; \backslash subset\; \backslash mathcal(x)$ such that :$\backslash forall\; V\; \backslash in\; \backslash mathcal(x)\; \backslash quad\; \backslash exists\; B\; \backslash in\; \backslash mathcal(x)\; \backslash mbox\; B\; \backslash subset\; V$. That is, for any neighbourhood $V$ we can find a neighbourhood $B$ in the neighbourhood basis that is contained in $V$. Conversely, as with any filter base, the local basis allows to get back the corresponding neighbourhood filter as $\backslash mathcal(x)\; =\backslash left\backslash$.〔 (See Chapter 2, Section 4)〕 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「neighbourhood system」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.