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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 (mathematics) ： ウィキペディア英語版 Neighbourhood (mathematics) In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where one can move that point some amount without leaving the set. This concept is closely related to the concepts of open set and interior. == Definition == If $X$ is a topological space and $p$ is a point in $X$, a neighbourhood of $p$ is a subset $V$ of $X$ that includes an open set $U$ containing $p$, :$p\; \backslash in\; U\; \backslash subseteq\; V.$ This is also equivalent to $p\backslash in\; X$ being in the interior of $V$. Note that the neighbourhood $V$ need not be an open set itself. If $V$ is open it is called an open neighbourhood. Some scholars require that neighbourhoods be open, so it is important to note conventions. A set that is a neighbourhood of each of its points is open since it can be expressed as the union of open sets containing each of its points. The collection of all neighbourhoods of a point is called the neighbourhood system at the point. If $S$ is a subset of $X$ then a neighbourhood of $S$ is a set $V$ that includes an open set $U$ containing $S$. It follows that a set $V$ is a neighbourhood of $S$ if and only if it is a neighbourhood of all the points in $S$. Furthermore, it follows that $V$ is a neighbourhood of $S$ iff $S$ is a subset of the interior of $V$. 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 (mathematics)」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.