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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 Homeotopy ： ウィキペディア英語版 Homeotopy In algebraic topology, an area of mathematics, a homeotopy group of a topological space is a homotopy group of the group of self-homeomorphisms of that space. ==Definition== The homotopy group functors $\backslash pi\_k$ assign to each path-connected topological space $X$ the group $\backslash pi\_k(X)$ of homotopy classes of continuous maps $S^k\backslash to\; X.$ Another construction on a space $X$ is the group of all self-homeomorphisms $X\; \backslash to\; X$, denoted $(X).$ If ''X'' is a locally compact, locally connected Hausdorff space then a fundamental result of R. Arens says that $(X)$ will in fact be a topological group under the compact-open topology. Under the above assumptions, the homeotopy groups for $X$ are defined to be: :$HME\_k(X)=\backslash pi\_k((X)).$ Thus $HME\_0(X)=\backslash pi\_0((X))=MCG^$ *(X) is the extended mapping class group for $X.$ In other words, the extended mapping class group is the set of connected components of $(X)$ as specified by the functor $\backslash pi\_0.$ 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「Homeotopy」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.