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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 Mesocompact space ： ウィキペディア英語版 Mesocompact space In mathematics, in the field of general topology, a topological space is said to be mesocompact if every open cover has a ''compact-finite'' open refinement.〔Hart, Nagata & Vaughan, p200〕 That is, given any open cover, we can find an open refinement with the property that every compact set meets only finitely many members of the refinement.〔Pearl, p23〕 The following facts are true about mesocompactness: * Every compact space, and more generally every paracompact space is mesocompact. This follows from the fact that any locally finite cover is automatically compact-finite. * Every mesocompact space is metacompact, and hence also orthocompact. This follows from the fact that points are compact, and hence any compact-finite cover is automatically point finite. ==Notes== 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「Mesocompact space」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.