The fundamental group of \(X\) at \(x_0\) is \[\pi_1(X, x_0) \;:=\; \bigl\{[\gamma] \mid \gamma \text{ is a loop based at } x_0\bigr\}\] equipped with the group operation of concatenation: \[[\gamma] \cdot [\delta] := [\gamma * \delta], \qquad (\gamma * \delta)(s) := \begin{cases} \gamma(2s) & s \in [0,\tfrac{1}{2}] \\ \delta(2s-1) & s \in [\tfrac{1}{2},1] \end{cases}\] The identity element is the class of the constant loop \([c_{x_0}]\), and the inverse of \([\gamma]\) is \([\bar\gamma]\) where \(\bar\gamma(s) := \gamma(1-s)\).
В рыболовной сети нашли 15-метровую тушу редкого кита20:45
，详情可参考新收录的资料
你是否也有过慢性腰背痛、神经痛的困扰，吃止痛药怕副作用，理疗效果又甚微？全球超 20% 的人受慢性疼痛折磨，却一直缺安全有效的解法，而这项新研究就为慢性疼痛的无创治疗找到了全新方向。
Российская пенсионерка купила золота на 19 миллионов рублей14:50，这一点在新收录的资料中也有详细论述
Опасность северокорейских хакеров для России оценили07:45，推荐阅读新收录的资料获取更多信息
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