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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 homotopy extension property ： ウィキペディア英語版 homotopy extension property In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space. ==Definition== Let $X\backslash ,\backslash !$ be a topological space, and let $A\; \backslash subset\; X$. We say that the pair $(X,A)\backslash ,\backslash !$ has the homotopy extension property if, given a homotopy $f\_t\backslash colon\; A\; \backslash rightarrow\; Y$ and a map $F\_0\backslash colon\; X\; \backslash rightarrow\; Y$ such that $F\_0\; |\_A\; =\; f\_0$, there exists an ''extension'' of $F\_0$ to a homotopy $F\_t\backslash colon\; X\; \backslash rightarrow\; Y$ such that $F\_t|\_A\; =\; f\_t$. 〔A. Dold, ''Lectures on Algebraic Topology'', pp. 84, Springer ISBN 3-540-58660-1〕 That is, the pair $(X,A)\backslash ,\backslash !$ has the homotopy extension property if any map $G\backslash colon\; ((X\backslash times\; \backslash )\; \backslash cup\; (A\backslash times\; I))\; \backslash rightarrow\; Y$ can be extended to a map $G\text{'}\backslash colon\; X\backslash times\; I\; \backslash rightarrow\; Y$ (i.e. $G\backslash ,\backslash !$ and $G\text{'}\backslash ,\backslash !$ agree on their common domain). If the pair has this property only for a certain codomain $Y\backslash ,\backslash !$, we say that $(X,A)\backslash ,\backslash !$ has the homotopy extension property with respect to $Y\backslash ,\backslash !$. 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「homotopy extension property」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.