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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 Antiisomorphism ： ウィキペディア英語版 Antiisomorphism In Category theory, a branch of formal mathematics, an antiisomorphism (or anti-isomorphism) between structured sets ''A'' and ''B'' is an isomorphism from ''A'' to the opposite of ''B'' (or equivalently from the opposite of ''A'' to ''B''). If there exists an antiisomorphism between two structures, they are ''antiisomorphic.'' Intuitively, to say that two mathematical structures are ''antiisomorphic'' is to say that they are basically opposites of one another. The concept is particularly useful in an algebraic setting, as, for instance, when applied to rings. ==Simple example== Let ''A'' be the binary relation (or directed graph) consisting of elements and binary relation $\backslash rightarrow$ defined as follows: * $1\; \backslash rightarrow\; 2;$ * $1\; \backslash rightarrow\; 3;$ * $2\; \backslash rightarrow\; 1.$ Let ''B'' be the binary relation set consisting of elements and binary relation $\backslash Rightarrow$ defined as follows: * $b\; \backslash Rightarrow\; a;$ * $c\; \backslash Rightarrow\; a;$ * $a\; \backslash Rightarrow\; b.$ Note that the opposite of ''B'' (called ''B''op) is the same set of elements with the opposite binary relation $\backslash Leftarrow$ (that is, reverse all the arcs of the directed graph): * $b\; \backslash Leftarrow\; a;$ * $c\; \backslash Leftarrow\; a;$ * $a\; \backslash Leftarrow\; b.$ If we replace ''a'', ''b'', and ''c'' with 1, 2, and 3 respectively, we will see that each rule in ''B''op is the same as some rule in ''A''. That is, we can define an isomorphism $\backslash phi$ from ''A'' to ''B''op by This $\backslash phi$ is an antiisomorphism between ''A'' and ''B''. 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「Antiisomorphism」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.