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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 Poset topology ： ウィキペディア英語版 Poset topology In mathematics, the poset topology associated with a partially ordered set ''S'' (or poset for short) is the Alexandrov topology (open sets are upper sets) on the poset of finite chains of S, ordered by inclusion. Let V be a set of vertices. An abstract simplicial complex Δ is a set of finite sets of vertices, known as faces $\backslash sigma\; \backslash subseteq\; V$, such that ::$\backslash forall\; \backslash rho,\; \backslash sigma.\; \backslash ;\backslash \; \backslash rho\; \backslash subseteq\; \backslash sigma\; \backslash in\; \backslash Delta\; \backslash Rightarrow\; \backslash rho\; \backslash in\; \backslash Delta$ Given a simplicial complex Δ as above, we define a (point set) topology on Δ by letting a subset $\backslash Gamma\; \backslash subseteq\; \backslash Delta$ be closed if and only if Γ is a simplicial complex: ::$\backslash forall\; \backslash rho,\; \backslash sigma.\; \backslash ;\backslash \; \backslash rho\; \backslash subseteq\; \backslash sigma\; \backslash in\; \backslash Gamma\; \backslash Rightarrow\; \backslash rho\; \backslash in\; \backslash Gamma$ This is the Alexandrov topology on the poset of faces of Δ. The order complex associated with a poset, S, has the underlying set of S as vertices, and the finite chains (i.e. finite totally ordered subsets) of S as faces. The poset topology associated with a poset S is the Alexandrov topology on the order complex associated with S. ==See also== * Topological combinatorics 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「Poset 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.