翻訳と辞書 Words near each other ・ Sepia stingray ・ Sepia subplana ・ Sepia subtenuipes ・ Sepia tala ・ Sepia tanybracheia ・ Sepia Tears ~midwinter's reprise~ ・ Separative work units ・ Separator ・ Separator (electricity) ・ Separator (milk) ・ Separator (oil production) ・ Separatory funnel ・ Separatrix ・ Separatrix (dynamical systems) ・ Separdan, Siahkal ・ Separoid ・ Separowo ・ Separu ・ Separuh Aku ・ Sepasar ・ Sepasitik ・ Sepaste ・ Sepat ・ Sepatan ・ Sepatan Timur ・ Sepatini River ・ Sepci ・ SEPCO ・ SEPCO3 ・ Sepe 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 Separoid ： ウィキペディア英語版 Separoid In mathematics, a separoid is a binary relation between disjoint sets which is stable as an ideal in the canonical order induced by inclusion. Many mathematical objects which appear to be quite different, find a common generalisation in the framework of separoids; e.g., graphs, configurations of convex sets, oriented matroids, and polytopes. Any countable category is an induced subcategory of separoids when they are endowed with homomorphisms () (viz., mappings that preserve the so-called ''minimal Radon partitions''). In this general framework, some results and invariants of different categories turn out to be special cases of the same aspect; e.g., the pseudoachromatic number from graph theory and the Tverberg theorem from combinatorial convexity are simply two faces of the same aspect, namely, complete colouring of separoids. == The axioms == A separoid () is a set $S$ endowed with a binary relation $\backslash mid\backslash \; \backslash subseteq2^S\backslash times2^S$ on its power set, which satisfies the following simple properties for $A,B\backslash subseteq\; S$: : $A\backslash mid\; B\backslash Leftrightarrow\; B\backslash mid\; A,$ : $A\backslash mid\; B\backslash Rightarrow\; A\backslash cap\; B=\backslash varnothing,$ : $A\backslash mid\; B\; \backslash hbox\; A\text{'}\backslash subset\; A\backslash Rightarrow\; A\text{'}\backslash mid\; B.$ A related pair $A\backslash mid\; B$ is called a separation and we often say that ''A is separated from B''. It is enough to know the ''maximal'' separations to reconstruct the separoid. A mapping $\backslash varphi\backslash colon\; S\backslash to\; T$ is a morphism of separoids if the preimages of separations are separations; that is, for $A,B\backslash subseteq\; T$ : $A\backslash mid\; B\backslash Rightarrow\backslash varphi^(A)\backslash mid\backslash varphi^(B).$ 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「Separoid」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.