翻訳と辞書 Words near each other ・ Prokop Sieniawski (d. 1627) ・ Prokop the Great ・ Prokop valley ・ Prokopenko ・ Prokopia ・ Prokopije Čokorilo ・ Prokopios Lazaridis ・ Projective cone ・ Projective connection ・ Projective cover ・ Projective differential geometry ・ Projective frame ・ Projective geometry ・ Projective group (disambiguation) ・ Projective harmonic conjugate ・ Projective hierarchy ・ Projective Hilbert space ・ Projective identification ・ Projective line ・ Projective line over a ring ・ Projective linear group ・ Projective module ・ Projective object ・ Projective orthogonal group ・ Projective plane ・ Projective polyhedron ・ Projective range ・ Projective representation ・ Projective set (disambiguation) ・ Projective Set (game) 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 Projective hierarchy ： ウィキペディア英語版 Projective hierarchy In the mathematical field of descriptive set theory, a subset $A$ of a Polish space $X$ is projective if it is $\backslash boldsymbol^1\_n$ for some positive integer $n$. Here $A$ is * $\backslash boldsymbol^1\_1$ if $A$ is analytic * $\backslash boldsymbol^1\_n$ if the complement of $A$, $X\backslash setminus\; A$, is $\backslash boldsymbol^1\_n$ * $\backslash boldsymbol^1\_$ if there is a Polish space $Y$ and a $\backslash boldsymbol^1\_n$ subset $C\backslash subseteq\; X\backslash times\; Y$ such that $A$ is the projection of $C$; that is, $A=\backslash$ The choice of the Polish space $Y$ in the third clause above is not very important; it could be replaced in the definition by a fixed uncountable Polish space, say Baire space or Cantor space or the real line. == Relationship to the analytical hierarchy == There is a close relationship between the relativized analytical hierarchy on subsets of Baire space (denoted by lightface letters $\backslash Sigma$ and $\backslash Pi$) and the projective hierarchy on subsets of Baire space (denoted by boldface letters $\backslash boldsymbol$ and $\backslash boldsymbol$). Not every $\backslash boldsymbol^1\_n$ subset of Baire space is $\backslash Sigma^1\_n$. It is true, however, that if a subset ''X'' of Baire space is $\backslash boldsymbol^1\_n$ then there is a set of natural numbers ''A'' such that ''X'' is $\backslash Sigma^\_n$. A similar statement holds for $\backslash boldsymbol^1\_n$ sets. Thus the sets classified by the projective hierarchy are exactly the sets classified by the relativized version of the analytical hierarchy. This relationship is important in effective descriptive set theory. A similar relationship between the projective hierarchy and the relativized analytical hierarchy holds for subsets of Cantor space and, more generally, subsets of any effective Polish space. 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「Projective hierarchy」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.