翻訳と辞書 Words near each other ・ N-bomb ・ N-Bromosuccinimide ・ N-Butanol ・ N-Butylamine ・ N-Butyllithium ・ N-carbamoyl-D-amino acid hydrolase ・ N-carbamoyl-L-amino-acid hydrolase ・ N-carbamoylase ・ N-carbamoylputrescine amidase ・ N-carbamoylsarcosine amidase ・ N-category number ・ N-Chlorosuccinimide ・ N-class blimp ・ N-class ferry ・ N-Coded Music ・ N-connected ・ N-Control Avenger ・ N-curve ・ N-Cyclohexyl-2-pyrrolidone ・ N-Desalkylflurazepam ・ N-deterrence ・ N-diaeresis ・ N-dimensional sequential move puzzle ・ N-Dubz ・ N-Dubz Christmas Party ・ N-Dubz discography ・ N-electron valence state perturbation theory ・ N-ellipse ・ N-end rule ・ N-entity 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 N-connected ： ウィキペディア英語版 N-connected In the mathematical branch of algebraic topology, specifically homotopy theory, ''n''-connectedness is a way to say that a space vanishes or that a map is an isomorphism "up to dimension ''n,'' in homotopy". ==''n''-connected space== A topological space ''X'' is said to be ''n''-connected when it is non-empty, path-connected, and its first ''n'' homotopy groups vanish identically, that is :$\backslash pi\_i(X)\; \backslash equiv\; 0~,\; \backslash quad\; 1\backslash leq\; i\backslash leq\; n\; ,$ where the left-hand side denotes the ''i''-th homotopy group. The requirements of being non-empty and path-connected can be interpreted as (−1)-connected and 0-connected, respectively, which is useful in defining 0-connected and 1-connected maps, as below. The 0-''th homotopy set'' can be defined as: :$\backslash pi\_0(X,$ *) := ((X, *) ). This is only a pointed set, not a group, unless ''X'' is itself a topological group; the distinguished point is the class of the trivial map, sending ''S''0 to the base point of ''X''. Using this set, a space is 0-connected if and only if the 0th homotopy set is the one-point set. The definition of homotopy groups and this homotopy set require that ''X'' be pointed (have a chosen base point), which cannot be done if ''X'' is empty. A topological space ''X'' is path-connected if and only if its 0-th homotopy group vanishes identically, as path-connectedness implies that any two points ''x1'' and ''x2'' in ''X'' can be connected with a continuous path which starts in ''x1'' and ends in ''x2'', which is equivalent to the assertion that every mapping from ''S0'' (a discrete set of two points) to ''X'' can be deformed continuously to a constant map. With this definition, we can define ''X'' to be n-connected if and only if :$\backslash pi\_i(X)\; \backslash equiv\; 0,\; \backslash quad\; 0\backslash leq\; i\backslash leq\; n.$ 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「N-connected」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.