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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 Development (topology) ： ウィキペディア英語版 Development (topology) In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms. Let $X$ be a topological space. A development for $X$ is a countable collection $F\_1,\; F\_2,\; \backslash ldots$ of open coverings of $X$, such that for any closed subset $C\; \backslash subset\; X$ and any point $p$ in the complement of $C$, there exists a cover $F\_j$ such that no element of $F\_j$ which contains $p$ intersects $C$. A space with a development is called developable. A development $F\_1,\; F\_2,\backslash ldots$ such that $F\_\backslash subset\; F\_i$ for all $i$ is called a nested development. A theorem from Vickery states that every developable space in fact has a nested development. If $F\_$ is a refinement of $F\_i$, for all $i$, then the development is called a refined development. Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable. ==References== * * * 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「Development (topology)」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.