18:15, 9 марта 2026Мир
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，这一点在新收录的资料中也有详细论述
今年的征文活动更有创意，「只能用 AI」和「不能用 AI」两大赛道激情 PK，硅基生物和碳基生物都将决出各自领域的佼佼者。我们会在征文结束后统一组织投票活动，但在正式投票之前，如果你喜欢这篇文章，不妨通过充电或评论的方式支持作者，让内容创作者获得更多维度的鼓励。
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 \(\bar\gamma(s) := \gamma(1-s)\).
And that’s concretely testable and verifiable.