Irreducible component

Summary

A topological space is irreducible when it is nonempty and is not the union of two proper closed subsets. An irreducible component of a space is a maximal irreducible subset. In a Noetherian space, such as an algebraic set with its Zariski topology, there are only finitely many irreducible components. The space is their union. This splits every algebraic set into irreducible pieces, the varieties.