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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 Constructible set (topology) ： ウィキペディア英語版 Constructible set (topology) :''For a Gödel constructive set, see constructible universe.'' In topology, a constructible set in a topological space is a finite union of locally closed sets. (A set is locally closed if it is the intersection of an open set and closed set, or equivalently, if it is open in its closure.) Constructible sets form a Boolean algebra (i.e., it is closed under finite union and complementation.) In fact, the constructible sets are precisely the Boolean algebra generated by open sets and closed sets; hence, the name "constructible". The notion appears in classical algebraic geometry. Chevalley's theorem (EGA IV, 1.8.4.) states: Let $f:\; X\; \backslash to\; Y$ be a morphism of finite presentation of schemes. Then the image of any constructible set under ''f'' is constructible. In particular, the image of a variety need not be a variety, but is (under the assumptions) always a constructible set. For example, the map $\backslash mathbf\; A^2\; \backslash rightarrow\; \backslash mathbf\; A^2$ that sends $(x,y)$ to $(x,xy)$ has image the set $\backslash \; \backslash cup\; \backslash$, which is not a variety, but is constructible. In a topological space, every constructible set contains a dense open subset of its closure.〔Jinpeng An (2012). ("Rigid geometric structures, isometric actions, and algebraic quotients" ). Geom. Dedicata 157: 153–185.〕 == See also == *Constructible topology *Constructible sheaf 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「Constructible set (topology)」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.