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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 Exhaustion by compact sets ： ウィキペディア英語版 Exhaustion by compact sets In mathematics, especially analysis, exhaustion by compact sets of an open set ''E'' in the Euclidean space R''n'' (or a manifold with countable base) is an increasing sequence of compact sets $K\_j$, where by increasing we mean $K\_j$ is a subset of $K\_$, with the limit (union) of the sequence being ''E''. Sometimes one requires the sequence of compact sets to satisfy one more property— that $K\_j$ is contained in the interior of $K\_$ for each $j$. This, however, is dispensed in R''n'' or a manifold with countable base. For example, consider a unit open disk and the concentric closed disk of each radius inside. That is let $E\; =\; \backslash$ and $K\_j\; =\; \backslash$. Then taking the limit (union) of the sequence $K\_j$ gives ''E''. The example can be easily generalized in other dimensions. ==See also== *σ-compact space 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「Exhaustion by compact sets」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.