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1. www.fffdann.com › portalFFF团簡

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   这下面举了两个例子. 第一个例子是说：对于每个拓扑空间X，我们都有一个点集\pi_0 (X)。 这个点集是X上所有点的一种等价类。 这个等价类的定义是，假设我们有一个经典的拓扑空间：R的局部： [0,1]。 以及拓扑空间X。 假设我们有个 [0,1]到X的连续映射p，令p (0)=x_1属于点集X，p (1)=x_2属于点集X。 那么我们就把他叫做：点x_1在“\pi_0 (X)的意义下”等价于点x_2。 最后，这些点的全部等价类构成了一个集合：\pi_0 (X)。 这就是一个不变量的例子。 第二个例子是基本群或者叫做在x点上的第一同伦群：\pi_1 (X,x)。 也是说： 对于每个拓扑空间X，我们任取一个在 例子一 意义下等价的点，都可以构造这样一个集合。

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