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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 Collapse (topology) ： ウィキペディア英語版 Collapse (topology) In topology, a branch of mathematics, collapse is a concept due to J. H. C. Whitehead.〔Whitehead, J.H.C. (1938) ''Simplical spaces, nuclei and m-groups'', Proceedings of the London Mathematical Society 45, pp 243–327〕 == Definition == Let $K$ be an abstract simplicial complex. Suppose that $\backslash tau,\; \backslash sigma\; \backslash in\; K$ such that the following two conditions are satisfied: (i) $\backslash tau\; \backslash subset\; \backslash sigma$, in particular ; (ii) $\backslash sigma$ is a maximal face of K and no other maximal face of K contains $\backslash tau$, then $\backslash tau$ is called a free face. A simplicial collapse of K is the removal of all simplices $\backslash gamma$ such that $\backslash tau\; \backslash subseteq\backslash gamma\; \backslash subseteq\; \backslash sigma$, where $\backslash tau$ is a free face. If additionally we have dim τ = dim σ-1, then this is called an elementary collapse. A simplicial complex that has a sequence of collapses leading to a point is called collapsible. Every collapsible complex is contractible, but the converse is not true. This definition can be extended to CW-complexes and is the basis for the concept of simple-homotopy equivalence.〔Cohen, M.M. (1973) ''A Course in Simple-Homotopy Theory'', Springer-Verlag New York〕 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「Collapse (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.