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Seifert-Van Kampen theorem

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Statement

Let $\text{[math]}$ be a topological space, and $\text{[math]}$ be open sets such that $\text{[math]}$ , and $\text{[math]}$ , $\text{[math]}$ and $\text{[math]}$ are path-connected. Take a basepoint $\text{[math]}$ with inclusion maps:

$\text{[math]}$

then the following diagram is a pushout:

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