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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 : The closed sets are : 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 : 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 : 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
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