翻訳と辞書 Words near each other ・ Local Energy Scotland ・ Local enterprise company ・ Local Enterprise Investment Centre ・ Local enterprise partnership ・ Local Environment ・ Local Euler characteristic formula ・ Local exchange carrier ・ Local exchange trading system ・ Local extinction ・ Local feature size ・ Local federation ・ Local Ferries in Suffolk ・ Local field ・ Local field potential ・ Local Fields ・ Local flatness ・ Local food ・ Local Food Hero ・ Local Food Plus ・ Local football championships of Greece ・ Local franchise authority ・ Local Futures ・ Local Gentry ・ Local Geodiversity Action Plan ・ Local gigantism ・ Local Governance (Scotland) Act 2004 ・ Local governance in Kerala ・ Local government ・ Local government (ancient Roman) ・ Local Government (Areas) Act 1948 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 Local flatness ： ウィキペディア英語版 Local flatness In topology, a branch of mathematics, local flatness is a property of a submanifold in a topological manifold of larger dimension. In the category of topological manifolds, locally flat submanifolds play a role similar to that of embedded submanifolds in the category of smooth manifolds. Suppose a ''d'' dimensional manifold ''N'' is embedded into an ''n'' dimensional manifold ''M'' (where ''d'' < ''n''). If $x\; \backslash in\; N,$ we say ''N'' is locally flat at ''x'' if there is a neighborhood $U\; \backslash subset\; M$ of ''x'' such that the topological pair $(U,\; U\backslash cap\; N)$ is homeomorphic to the pair $(\backslash mathbb^n,\backslash mathbb^d)$, with a standard inclusion of $\backslash mathbb^d$ as a subspace of $\backslash mathbb^n$. That is, there exists a homeomorphism $U\backslash to\; R^n$ such that the image of $U\backslash cap\; N$ coincides with $\backslash mathbb^d$. The above definition assumes that, if ''M'' has a boundary, ''x'' is not a boundary point of ''M''. If ''x'' is a point on the boundary of ''M'' then the definition is modified as follows. We say that ''N'' is locally flat at a boundary point ''x'' of ''M'' if there is a neighborhood $U\backslash subset\; M$ of ''x'' such that the topological pair $(U,\; U\backslash cap\; N)$ is homeomorphic to the pair $(\backslash mathbb^n\_+,\backslash mathbb^d)$, where $\backslash mathbb^n\_+$ is a standard half-space and $\backslash mathbb^d$ is included as a standard subspace of its boundary. In more detail, we can set $\backslash mathbb^n\_+\; =\; \backslash$ and $\backslash mathbb^d\; =\; \backslash =\backslash cdots=y\_n=0\backslash \}$. We call ''N'' locally flat in ''M'' if ''N'' is locally flat at every point. Similarly, a map $\backslash chi\backslash colon\; N\backslash to\; M$ is called locally flat, even if it is not an embedding, if every ''x'' in ''N'' has a neighborhood ''U'' whose image $\backslash chi(U)$ is locally flat in ''M''. Local flatness of an embedding implies strong properties not shared by all embeddings. Brown (1962) proved that if ''d'' = ''n'' − 1, then ''N'' is collared; that is, it has a neighborhood which is homeomorphic to ''N'' × () with ''N'' itself corresponding to ''N'' × 1/2 (if ''N'' is in the interior of ''M'') or ''N'' × 0 (if ''N'' is in the boundary of ''M''). ==See also== *Neat submanifold 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「Local flatness」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.