翻訳と辞書 Words near each other ・ Delta rule ・ Delta Sagittae ・ Delta Sagittarii ・ Delta Sailplane Nomad ・ Delta scale ・ Delta Scientific Corporation ・ Delta Scorpii ・ Delta Sculptoris ・ Delta Scuti ・ Delta Scuti variable ・ Delta Secondary School ・ Delta Secondary School (Delta, British Columbia) ・ Delta Secondary School (Hamilton, Ontario) ・ Delta Secondary School Windhoek ・ Delta Serpentis ・ Delta set ・ Delta Sextantis ・ Delta Shuttle ・ Delta Sigma ・ Delta Sigma Chi ・ Delta Sigma Delta ・ Delta Sigma Epsilon ・ Delta Sigma Epsilon (sorority) ・ Delta Sigma Phi ・ Delta Sigma Pi ・ Delta Sigma Sorority ・ Delta Sigma Theta ・ Delta Sigma Xi ・ Delta Single Member Constituency ・ Delta sleep-inducing peptide 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 Delta set ： ウィキペディア英語版 Delta set In mathematics, a delta set (or Δ-set) ''S'' is a combinatorial object that is useful in the construction and triangulation of topological spaces, and also in the computation of related algebraic invariants of such spaces. A delta set is somewhat more general than a simplicial complex, yet not quite as general as a simplicial set. ==Definition and related data== Formally, a Δ-set is a sequence of sets $\backslash \_^$ together with maps :$d\_i\; :\; S\_\; \backslash rightarrow\; S\_n$ with ''i'' = 0,1,...,''n'' + 1 for ''n'' ≥ 1 that satisfy :$d\_i\; \backslash circ\; d\_j\; =\; d\_\; \backslash circ\; d\_i$ whenever ''i < j''. This definition generalizes the notion of a simplicial complex, where the $S\_n$ are the sets of ''n''-simplices, and the ''d''''i'' are the face maps. It is not as general as a simplicial set, since it lacks "degeneracies." Given $\backslash Delta$-sets ''S'' and ''T'', a map of $\backslash Delta$-sets is a collection :$\backslash \_^$ such that :$f\_n\; \backslash circ\; d\_i\; =\; d\_i\; \backslash circ\; f\_$ whenever both sides of the equation are defined. With this notion, we can define the category of Δ-sets, whose objects are $\backslash Delta$-sets and whose morphisms are maps of $\backslash Delta$-sets. Each $\backslash Delta$-set has a corresponding geometric realization, defined as :$|S|\; =\; \backslash left(\; \backslash coprod\_^\; S\_n\; \backslash times\; \backslash Delta^n\; \backslash right)/\_$ where we declare that : $(\backslash sigma,d^i\; t)\; \backslash sim\; (d\_i\; \backslash sigma,\; t)\; \backslash quad\; \backslash text\; \backslash quad\; \backslash sigma\; \backslash in\; S\_n,\; t\; \backslash in\; \backslash Delta^.$ Here, $\backslash Delta^n$ denotes the standard ''n''-simplex, and :$d^i\; :\; \backslash Delta^\; \backslash rightarrow\; \backslash Delta^n$ is the inclusion of the ''i''-th face. The geometric realization is a topological space with the quotient topology. The geometric realization of a $\backslash Delta$-set ''S'' has a natural filtration : $|S|\_0\; \backslash subset\; |S|\_1\; \backslash subset\; \backslash cdots\; \backslash subset\; |S|,$ where :$|S|\_N\; =\; \backslash left(\; \backslash coprod\_^\; S\_n\; \backslash times\; \backslash Delta^n\; \backslash right)/\_$ is a "restricted" geometric realization. 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「Delta 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.