Seifert-van Kampen theorem
= Seifert-van Kampen theorem
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= van Kampen theorem
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For a suitably path-connected open cover $X=U\cup V$, the fundamental group of $X$ is the pushout of the homomorphisms from $\pi_1(U\cap V)$ to $\pi_1(U)$ and $\pi_1(V)$.