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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 wedge sum ： ウィキペディア英語版 wedge sum In topology, the wedge sum is a "one-point union" of a family of topological spaces. Specifically, if ''X'' and ''Y'' are pointed spaces (i.e. topological spaces with distinguished basepoints ''x''0 and ''y''0) the wedge sum of ''X'' and ''Y'' is the quotient space of the disjoint union of ''X'' and ''Y'' by the identification ''x''0 ∼ ''y''0: :$X\backslash vee\; Y\; =\; (X\backslash amalg\; Y)\backslash ;/,\backslash ,$ where ∼ is the equivalence closure of the relation . More generally, suppose (''X''''i'')''i'' ∈ ''I'' is a family of pointed spaces with basepoints . The wedge sum of the family is given by: :$\backslash bigvee\_i\; X\_i\; =\; \backslash coprod\_i\; X\_i\backslash ;/,\backslash ,$ where ∼ is the equivalence relation . In other words, the wedge sum is the joining of several spaces at a single point. This definition is sensitive to the choice of the basepoints , unless the spaces are homogeneous. The wedge sum is again a pointed space, and the binary operation is associative and commutative (up to isomorphism). Sometimes the wedge sum is called the wedge product, but this is not the same concept as the exterior product, which is also often called the wedge product. ==Examples== The wedge sum of two circles is homeomorphic to a figure-eight space. The wedge sum of ''n'' circles is often called a ''bouquet of circles'', while a wedge product of arbitrary spheres is often called a bouquet of spheres. A common construction in homotopy is to identify all of the points along the equator of an ''n''-sphere $S^n$. Doing so results in two copies of the sphere, joined at the point that was the equator: :$S^n/\; =\; S^n\; \backslash vee\; S^n$ Let $\backslash Psi$ be the map $\backslash Psi:S^n\backslash to\; S^n\; \backslash vee\; S^n$, that is, of identifying the equator down to a single point. Then addition of two elements $f,g\backslash in\backslash pi\_n(X,x\_0)$ of the ''n''-dimensional homotopy group $\backslash pi\_n(X,x\_0)$ of a space ''X'' at the distinguished point $x\_0\backslash in\; X$ can be understood as the composition of $f$ and $g$ with $\backslash Psi$: :$f+g\; =\; (f\; \backslash vee\; g)\; \backslash circ\; \backslash Psi$ Here, $f$ and $g$ are understood to be maps, $f:S^n\backslash to\; X$ and similarly for $g$, which take a distinguished point $s\_0\backslash in\; S^n$ to a point $x\_0\backslash in\; X$. Note that the above defined the wedge sum of two functions, which was possible because $f(s\_0)=g(s\_0)=x\_0$, which was the point that is equivalenced in the wedge sum of the underlying spaces. 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「wedge sum」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.