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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 Restricted product ： ウィキペディア英語版 Restricted product In mathematics, the restricted product is a construction in the theory of topological groups. Let $I$ be an indexing set; $S$ a finite subset of $I$. If for each $i\backslash in\; I$, $G\_i$ is a locally compact group, and for each $i\backslash in\; I\backslash backslash\; S$, $K\_i\; \backslash subset\; G\_i$ is an open compact subgroup, then the restricted product : $\text{'}\; G\_i\backslash ,$ is the subset of the product of the $G\_i$'s consisting of all elements $(g\_i)\_$ such that $g\_i\; \backslash in\; K\_i$ for all but finitely many $i\backslash in\; I\backslash backslash\; S$. This group is given the topology whose basis of open sets are those of the form : $\backslash prod\_i\; A\_i\backslash ,,$ where $A\_i$ is open in $G\_i$ and $A\_i\; =\; K\_i$ for all but finitely many $i$. One can easily prove that the restricted product is itself a locally compact group. The best known example of this construction is that of the adele ring and idele group of a global field. ==See also== *Direct sum 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「Restricted product」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.