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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 Mapping cone (topology) ： ウィキペディア英語版 Mapping cone (topology) In mathematics, especially homotopy theory, the mapping cone is a construction $C\_f$ of topology, analogous to a quotient space. It is also called the homotopy cofiber, and also notated $Cf$. ==Definition== Given a map $f\backslash colon\; X\; \backslash to\; Y$, the mapping cone $C\_f$ is defined to be the quotient topological space of $(X\; \backslash times\; I)\; \backslash sqcup\; Y$ with respect to the equivalence relation $(x,\; 0)\; \backslash sim\; (x\text{'},0)\backslash ,$, $(x,1)\; \backslash sim\; f(x)\backslash ,$ on ''X''. Here $I$ denotes the unit interval () with its standard topology. Note that some (like May) use the opposite convention, switching 0 and 1. Visually, one takes the cone on ''X'' (the cylinder $X\; \backslash times\; I$ with one end (the 0 end) identified to a point), and glues the other end onto ''Y'' via the map ''f'' (the identification of the 1 end). Coarsely, one is taking the quotient space by the image of ''X,'' so ''Cf'' "=" ''Y''/''f''(''X''); this is not precisely correct because of point-set issues, but is the philosophy, and is made precise by such results as the homology of a pair and the notion of an ''n''-connected map. The above is the definition for a map of unpointed spaces; for a map of pointed spaces $f\backslash colon\; (X,x\_0)\; \backslash to\; (Y,y\_0),$ (so $f\backslash colon\; x\_0\; \backslash mapsto\; y\_0$), one also identifies all of $\backslash times\; I$; formally, $(x\_0,t)\; \backslash sim\; (x\_0,t\text{'})\backslash ,.$ Thus one end and the "seam" are all identified with $y\_0.$ 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「Mapping cone (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.