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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 Compactly generated group ： ウィキペディア英語版 Compactly generated group In mathematics, a compactly generated (topological) group is a topological group ''G'' which is algebraically generated by one of its compact subsets.〔.〕 This should not be confused with the unrelated notion (widely used in algebraic topology) of a compactly generated space -- one whose topology is generated (in a suitable sense) by its compact subspaces. == Definition == A topological group ''G'' is said to be compactly generated if there exists a compact subset ''K'' of ''G'' such that :$\backslash langle\; K\backslash rangle\; =\; \backslash bigcup\_)^n\; =\; G.$ So if ''K'' is symmetric, i.e. ''K'' = ''K'' −1, then :$G\; =\; \backslash bigcup\_\{n\; \backslash in\; \backslash mathbb\{N\}\}\; K^n.$ 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「Compactly generated group」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.