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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 Join (topology) ： ウィキペディア英語版 Join (topology) In topology, a field of mathematics, the join of two topological spaces ''A'' and ''B'', often denoted by $A\backslash star\; B$, is defined to be the quotient space :$(A\; \backslash times\; B\; \backslash times\; I)\; /\; R,\; \backslash ,$ where ''I'' is the interval (1 ) and ''R'' is the equivalence relation generated by :$(a,\; b\_1,\; 0)\; \backslash sim\; (a,\; b\_2,\; 0)\; \backslash quad\backslash mbox\; a\; \backslash in\; A\; \backslash mbox\; b\_1,b\_2\; \backslash in\; B,$ :$(a\_1,\; b,\; 1)\; \backslash sim\; (a\_2,\; b,\; 1)\; \backslash quad\backslash mbox\; a\_1,a\_2\; \backslash in\; A\; \backslash mbox\; b\; \backslash in\; B.$ At the endpoints, this collapses $A\backslash times\; B\backslash times\; \backslash$ to $A$ and $A\backslash times\; B\backslash times\; \backslash$ to $B$. Intuitively, $A\backslash star\; B$ is formed by taking the disjoint union of the two spaces and attaching a line segment joining every point in ''A'' to every point in ''B''. ==Properties== * The join is homeomorphic to sum of cartesian products of cones over spaces and spaces itself, where sum is taken over cartesian product of spaces: :$A\backslash star\; B\backslash cong\; C(A)\backslash times\; B\backslash cup\_\; C(B)\backslash times\; A.$ * Given basepointed CW complexes (''A'',''a''0) and (''B'',''b''0), the "reduced join" :$\backslash frac\; \backslash star\; B\}$ is homeomorphic to the reduced suspension :$\backslash Sigma(A\backslash wedge\; B)$ of the smash product. Consequently, since $\backslash star\; B\}$ is contractible, there is a homotopy equivalence :$A\backslash star\; B\backslash simeq\; \backslash Sigma(A\backslash wedge\; B).$ 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「Join (topology)」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.