Seifert–van Kampen theorem

In mathematics, the Seifert–van Kampen theorem of algebraic topology, sometimes just called van Kampen's theorem, expresses the structure of the fundamental group of a topological space ${\displaystyle X}$, in terms of the fundamental groups of two open, path-connected subspaces ${\displaystyle U}$ and ${\displaystyle V}$ that cover ${\displaystyle X}$. It can therefore be used for computations of the fundamental group of spaces that are constructed out of simpler ones.

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