In algebraic geometry, an **irreducible component** of a topological space, particularly a scheme or algebraic variety, is a maximal irreducible subset of that space. To elaborate: 1. **Irreducibility**: A topological space is considered irreducible if it cannot be expressed as the union of two or more nonempty closed subsets.
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An irreducible component is a maximal irreducible closed subset. Every algebraic variety is a finite union of its irreducible components.