Seifert–Van Kampen theorem

In mathematics, the Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), 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 that cover ${\displaystyle X}$. It can therefore be used for computations of the fundamental group of spaces that are constructed out of simpler ones.