翻訳と辞書 Words near each other ・ Sierosławiec ・ Sieroty ・ Sierowo ・ Sierpc ・ Sierpc County ・ Sierpe River ・ Sierpienica ・ Sierpin ・ Sierpinski (crater) ・ Sierpinski carpet ・ Sierpinski number ・ Sierpinski triangle ・ Sierpiński arrowhead curve ・ Sierpiński curve ・ Sierpiński set ・ Sierpiński space ・ Sierpiński's constant ・ Sierpnica ・ Sierpowo, Greater Poland Voivodeship ・ Sierpowo, Pomeranian Voivodeship ・ Sierpów ・ Sierpówko ・ Sierra ・ Sierra (Dollhouse) ・ Sierra (film) ・ Sierra (group) ・ Sierra (name) ・ Sierra (TV series) ・ Sierra Academy of Aeronautics ・ Sierra Aguilada Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sierpiński space ： ウィキペディア英語版 Sierpiński space In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wacław Sierpiński. The Sierpiński space has important relations to the theory of computation and semantics.〔An online paper, it explains the motivation, why the notion of “topology” can be applied in the investigation of concepts of the computer science. Alex Simpson: (Mathematical Structures for Semantics ). Chapter III: (Topological Spaces from a Computational Perspective ). The “References” section provides many online materials on domain theory.〕 ==Definition and fundamental properties== Explicitly, the Sierpiński space is a topological space ''S'' whose underlying point set is and whose open sets are :$\backslash \backslash \}.$ The closed sets are :$\backslash \backslash \}.$ So the singleton set is closed (but not open) and the set is open (but not closed). The closure operator on ''S'' is determined by :$\backslash overline,\backslash qquad\backslash overline.$ A finite topological space is also uniquely determined by its specialization preorder. For the Sierpiński space this preorder is actually a partial order and given by :$0\backslash leq\; 0,\backslash qquad\; 0\backslash leq\; 1,\backslash qquad\; 1\backslash leq\; 1.$ 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「Sierpiński 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.