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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 Simply connected at infinity ： ウィキペディア英語版 Simply connected at infinity In topology, a branch of mathematics, a topological space ''X'' is said to be simply connected at infinity if for all compact subsets ''C'' of ''X'', there is a compact set ''D'' in ''X'' containing ''C'' so that the induced map : $\backslash pi\_1(X-D)\; \backslash to\; \backslash pi\_1(X-C)\backslash ,$ is trivial. Intuitively, this is the property that loops far away from a small subspace of ''X'' can be collapsed, no matter how bad the small subspace is. The Whitehead manifold is an example of a 3-manifold that is contractible but not simply connected at infinity. Since this property is invariant under homeomorphism, this proves that the Whitehead manifold is not homeomorphic to R3. However, it is a theorem of John R. Stallings that for $n\; \backslash geq\; 5$, a contractible ''n''-manifold is homeomorphic to R''n'' precisely when it is simply connected at infinity. ==References== 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「Simply connected at infinity」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.