翻訳と辞書 Words near each other ・ Ranadi ・ Ranae ・ RaNae Bair ・ Ranafast ・ Ranagau ・ Ranaghan ・ Ranaghat ・ Ranaghat (Lok Sabha constituency) ・ Ranaghat College ・ Ranaghat Dakshin (Vidhan Sabha constituency) ・ Ranaghat I (community development block) ・ Ranaghat II (community development block) ・ Ranaghat railway station ・ Ranaghat subdivision ・ Ranaghat Uttar Paschim (Vidhan Sabha constituency) ・ Ran space ・ RAN Station 9, Pinkenba ・ Ran Tikiri Sina ・ Ran Vijay Singh ・ Ran Yong ・ Ran Yu-Yu ・ Ran Yunfei ・ Ran Zhi ・ Ran-D ・ Rana ・ Rana (1998 film) ・ Rana (disambiguation) ・ Rana (film) ・ Rana (genus) ・ Rana (name) 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 Ran space ： ウィキペディア英語版 Ran space In mathematics, the Ran space (or Ran's space) of a topological space ''X'' is a topological space $\backslash operatorname(X)$ whose underlying set is the set of all nonempty finite subsets of ''X'': for a metric space ''X'' the topology is given by Hausdorff distance. The notion is named after Ziv Ran. It seems the notion was first introduced and popularized by A. Beilinson and V. Drinfeld, Chiral algebras. In general, the topology of the Ran space is generated by sets : $\backslash$ for any disjoint open subsets $U\_i\; \backslash subset\; X,\; 1\; \backslash le\; i\; \backslash le\; m$. A theorem of Beilinson and Drinfeld states that the Ran space of a connected manifold is weakly contractible. There is an analog of a Ran space for a scheme:〔http://www.math.harvard.edu/~lurie/282ynotes/LectureVII-Stacks.pdf〕 the Ran prestack of a quasi-projective scheme ''X'' over a field ''k'', denoted by $\backslash operatorname(X)$, is the category where the objects are triples $(R,\; S,\; \backslash mu)$ consisting of a finitely generated ''k''-algebra ''R'', a nonempty set ''S'' and a map of sets $\backslash mu:\; S\; \backslash to\; X(R)$ and where a morphism $(R,\; S,\; \backslash mu)\; \backslash to\; (R\text{'},\; S\text{'},\; \backslash mu\text{'})$ consists of a ''k''-algebra homomorphism $R\; \backslash to\; R\text{'}$, a surjective map $S\; \backslash to\; S\text{'}$ that commutes with $\backslash mu$ and $\backslash mu\text{'}$. Roughly, an ''R''-point of $\backslash operatorname(X)$ is a nonempty finite set of ''R''-rational points of ''X'' "with labels" given by $\backslash mu$. A theorem of Beilinson and Drinfeld continues to hold: $\backslash operatorname(X)$ is acyclic if ''X'' is connected. == Topological chiral homology == If ''F'' is a cosheaf on the Ran space $\backslash operatorname(M)$, then its space of global sections is called the topological chiral homology of ''M'' with coefficients in ''F''. If ''A'' is, roughly, a family of commutative algebras parametrized by points in ''M'', then there is a factorizable sheaf associated to ''A''. Via this construction, one also obtains the topological chiral homology with coefficients in ''A''. The construction is a generalization of Hochschild homology. 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.