翻訳と辞書 Words near each other ・ Extension and contraction of ideals ・ Extension bell ・ Extension by definitions ・ Extension conflict ・ Extension cord ・ Extension Ensemble ・ Extension Formation ・ Extension Gunners ・ Extension Language Kit ・ Extension mechanisms for DNS ・ Extension method ・ Extension neglect ・ Extension neural network ・ Extension of a Man ・ Extension of a polyhedron ・ Extension of a topological group ・ Extension of the Wish ・ Extension of University Education Act, 1959 ・ Extension Poly(A) Test ・ Extension Reef ・ Extension Scouting ・ Extension Service ・ Extension studies ・ Extension topology ・ Extension transference ・ Extension tube ・ Extension, British Columbia ・ Extension, Louisiana ・ Extensional context ・ Extensional definition Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Extension of a topological group ： ウィキペディア英語版 Extension of a topological group In mathematics, more specifically in topological groups, an extension of topological groups, or a topological extension, is a short exact sequence $0\backslash to\; H\backslash stackrel\; X\; \backslash stackrelG\backslash to\; 0$ where $H,\; X$ and $G$ are topological groups and $i$ and $\backslash pi$ are continuous homomorphisms which are also open onto their images. Every extension of topological group is therefore a group extension ==Classification of extensions of topological groups== We say that the topological extensions :$0\; \backslash rightarrow\; H\backslash stackrel\; X\backslash stackrel\; G\backslash rightarrow\; 0$ and :$0\backslash to\; H\backslash stackrel\; X\text{'}\backslash stackrel\; G\backslash rightarrow\; 0$ are equivalent (or congruent) if there exists a topological isomorphism $T:\; X\backslash to\; X\text{'}$ making commutative the diagram of Figure 1. We say that the topological extension :$0\; \backslash rightarrow\; H\backslash stackrel\; X\backslash stackrel\; G\backslash rightarrow\; 0$ is a ''split extension'' (or splits) if it is equivalent to the trivial extension :$0\; \backslash rightarrow\; H\backslash stackrel\; H\backslash times\; G\backslash stackrel\; G\backslash rightarrow\; 0$ where $i\_H:\; H\backslash to\; H\backslash times\; G$ is the natural inclusion over the first factor and $\backslash pi\_G:\; H\backslash times\; G\backslash to\; G$ is the natural projection over the second factor. It is easy to prove that the topological extension $0\; \backslash rightarrow\; H\backslash stackrel\; X\backslash stackrel\; G\backslash rightarrow\; 0$ splits if and only if there is a continuous homomorphism $R:\; X\; \backslash rightarrow\; H$ such that $R\backslash circ\; i$ is the identity map on $H$ Note that the topological extension $0\; \backslash rightarrow\; H\backslash stackrel\; X\backslash stackrel\; G\backslash rightarrow\; 0$ splits if and only if the subgroup $i(H)$ is a topological direct summand of $X$ 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「Extension of a topological group」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.