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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 Fσ set ： ウィキペディア英語版 Fσ set In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for ''fermé'' (''French'': closed) and σ for ''somme'' (''French'': sum, union).〔.〕 In metrizable spaces, every open set is an Fσ set.〔.〕 The complement of an Fσ set is a Gδ set.〔 In a metrizable space, any closed set is a Gδ set. The union of countably many Fσ sets is an Fσ set, and the intersection of finitely many Fσ sets is an Fσ set. Fσ is the same as $\backslash mathbf^0\_2$ in the Borel hierarchy. == Examples == Each closed set is an Fσ set. The set $\backslash mathbb$ of rationals is an Fσ set. The set $\backslash mathbb\backslash setminus\backslash mathbb$ of irrationals is not a Fσ set. In a Tychonoff space, each countable set is an Fσ set, because a point $$ is closed. For example, the set $A$ of all points $(x,y)$ in the Cartesian plane such that $x/y$ is rational is an Fσ set because it can be expressed as the union of all the lines passing through the origin with rational slope: :$A\; =\; \backslash bigcup\_\backslash \},$ where $\backslash mathbb$, is the set of rational numbers, which is a countable set. 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「Fσ set」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.