翻訳と辞書 Words near each other ・ Immigration reduction in the United States ・ Immigration reform ・ Immigration Reform and Control Act of 1986 ・ Immigration Restriction Act ・ Immigration Restriction Act 1901 ・ Immigration Restriction League ・ Immigration Service Ordinance ・ Immigration Services Tribunal ・ Immigration sign ・ Immigration Street ・ Immigration tariff ・ Immigration to Argentina ・ Immigration to Australia ・ Immersion ・ Immersion (album) ・ Immersion (mathematics) ・ Immersion (musicians) ・ Immersion (virtual reality) ・ Immersion baptism ・ Immersion blender ・ Immersion chiller ・ Immersion Composition Society ・ Immersion Corporation ・ Immersion exhibit ・ Immersion foot syndromes ・ Immersion Games ・ Immersion journalism ・ Immersion lithography ・ Immersion marketing ・ Immersion therapy 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 Immersion (mathematics) ： ウィキペディア英語版 Immersion (mathematics) :''For a closed immersion in algebraic geometry, see closed immersion.'' In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective.〔This definition is given by , , , , , , , .〕 Explicitly, ''f'' : ''M'' → ''N'' is an immersion if :$D\_pf\; :\; T\_p\; M\; \backslash to\; T\_N\backslash ,$ is an injective function at every point ''p'' of ''M'' (where ''TpX'' denotes the tangent space of a manifold ''X'' at a point ''p'' in ''X''). Equivalently, ''f'' is an immersion if its derivative has constant rank equal to the dimension of ''M'':〔This definition is given by , .〕 :$\backslash operatorname\backslash ,D\_p\; f\; =\; \backslash dim\; M.$ The function ''f'' itself need not be injective, only its derivative. A related concept is that of an embedding. A smooth embedding is an injective immersion ''f'' : ''M'' → ''N'' which is also a topological embedding, so that ''M'' is diffeomorphic to its image in ''N''. An immersion is precisely a local embedding – i.e. for any point ''x'' ∈ ''M'' there is a neighbourhood, ''U'' ⊂ ''M'', of ''x'' such that ''f'' : ''U'' → ''N'' is an embedding, and conversely a local embedding is an immersion.〔This kind of definition, based on local diffeomorphisms, is given by , .〕 For infinite dimensional manifolds, this is sometimes taken to be the definition of an immersion.〔This kind of infinite-dimensional definition is given by .〕 If ''M'' is compact, an injective immersion is an embedding, but if ''M'' is not compact then injective immersions need not be embeddings; compare to continuous bijections versus homeomorphisms. ==Regular homotopy== A regular homotopy between two immersions ''f'' and ''g'' from a manifold ''M'' to a manifold ''N'' is defined to be a differentiable function ''H'' : ''M'' × () → ''N'' such that for all ''t'' in (1 ) the function ''Ht'' : ''M'' → ''N'' defined by ''Ht''(''x'') = ''H''(''x'', ''t'') for all ''x'' ∈ ''M'' is an immersion, with ''H''0 = ''f'', ''H''1 = ''g''. A regular homotopy is thus a homotopy through immersions. 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「Immersion (mathematics)」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.