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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 Analytic set ： ウィキペディア英語版 Analytic set In descriptive set theory, a subset of a Polish space $X$ is an analytic set if it is a continuous image of a Polish space. These sets were first defined by and his student . == Definition == There are several equivalent definitions of analytic set. The following conditions on a subspace ''A'' of a Polish space are equivalent: *''A'' is analytic. *''A'' is empty or a continuous image of the Baire space ωω. *''A'' is a Suslin space, in other words ''A'' is the image of a Polish space under a continuous mapping. *''A'' is the continuous image of a Borel set in a Polish space. *''A'' is a Suslin set, the image of the Suslin operation. *There is a Polish space $Y$ and a Borel set $B\backslash subseteq\; X\backslash times\; Y$ such that $A$ is the projection of $B$; that is, : $A=\backslash .$ *''A'' is the projection of a closed set in the cartesian product of ''X'' times the Baire space. *''A'' is the projection of a ''G''δ set in the cartesian product of ''X'' times the Cantor space. An alternative characterization, in the specific, important, case that $X$ is Baire space ωω, is that the analytic sets are precisely the projections of trees on $\backslash omega\backslash times\backslash omega$. Similarly, the analytic subsets of Cantor space 2ω are precisely the projections of trees on $2\backslash times\backslash omega$. 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「Analytic 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.