Wedge Sum
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High Quality Content by WIKIPEDIA articles! 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 x0 and y0) the wedge sum of X and Y is the quotient of the disjoint union of X and Y by the identification x0 y0: Xvee Y = (Xamalg Y);/ ;{x_0 sim y_0} More generally, suppose (Xi)i I is a family of pointed spaces with basepoints {pi}. The wedge sum of the family is given by: bigvee_i X_i := coprod_i X_i;/ ;{p_isim p_j mid i,j in I}. In other words, the wedge sum is the…mehr

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High Quality Content by WIKIPEDIA articles! 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 x0 and y0) the wedge sum of X and Y is the quotient of the disjoint union of X and Y by the identification x0 y0: Xvee Y = (Xamalg Y);/ ;{x_0 sim y_0} More generally, suppose (Xi)i I is a family of pointed spaces with basepoints {pi}. The wedge sum of the family is given by: bigvee_i X_i := coprod_i X_i;/ ;{p_isim p_j mid i,j in I}. In other words, the wedge sum is the joining of several spaces at a single point. This definition of course depends on the choice of {pi} unless the spaces {Xi} are homogeneous.