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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 Prime integer topology ： ウィキペディア英語版 Prime integer topology In mathematics, and especially general topology, the prime integer topology and the relatively prime integer topology are examples of topologies on the set of positive whole numbers, i.e. the set }. To give the set Z+ a topology means to say which subsets of Z+ are "open", and to do so in a way that the following axioms are met:〔 # The union of open sets is an open set. # The finite intersection of open sets is an open set. # Z+ and the empty set ∅ are open sets. == Construction == Given two positive integers , define the following congruence class: :$U\_a(b)=\backslash \; \backslash \}$ Then the relatively prime integer topology is the topology generated from the basis :$\backslash mathfrak\; =\; \backslash$ and the prime integer topology is the sub-topology generated from the sub-basis :$\backslash mathfrak\; =\; \backslash \backslash \}$ The set of positive integers with the relatively prime integer topology or with the prime integer topology are examples of topological spaces that are Hausdorff but not regular.〔 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「Prime integer 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.