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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 Continuous group action ： ウィキペディア英語版 Continuous group action In topology, a continuous group action on a topological space ''X'' is a group action of a topological group ''G'' that is continuous: i.e., :$G\; \backslash times\; X\; \backslash to\; X,\; \backslash quad\; (g,\; x)\; \backslash mapsto\; g\; \backslash cdot\; x$ is a continuous map. Together with the group action, ''X'' is called a ''G''-space. If $f:\; H\; \backslash to\; G$ is a continuous group homomorphism of topological groups and if ''X'' is a ''G''-space, then ''H'' can act on ''X'' ''by restriction'': $h\; \backslash cdot\; x\; =\; f(h)\; x$, making ''X'' a ''H''-space. Often ''f'' is either an inclusion or a quotient map. In particular, any topological space may be thought of a ''G''-space via $G\; \backslash to\; 1$ (and ''G'' would act trivially.) Two basic operations are that of taking the space of points fixed by a subgroup ''H'' and that of forming a quotient by ''H''. We write $X^H$ for the set of all ''x'' in ''X'' such that $hx\; =\; x$. For example, if we write $F(X,\; Y)$ for the set of continuous maps from a ''G''-space ''X'' to another ''G''-space ''Y'', then, with the action $(g\; \backslash cdot\; f)(x)\; =\; g\; f(g^\; x)$, $F(X,\; Y)^G$ consists of ''f'' such that $f(g\; x)\; =\; g\; f(x)$; i.e., ''f'' is an equivariant map. We write $F\_G(X,\; Y)\; =\; F(X,\; Y)^G$. Note, for example, for a ''G''-space ''X'' and a closed subgroup ''H'', $F\_G(G/H,\; X)\; =\; X^H$. == References == *John Greenlees, Peter May, ''(Equivariant stable homotopy theory )'' 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「Continuous group action」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.