Definition:Irreducible Component

Definition
Let $T = \struct {S, \tau}$ be a topological space.

A subspace $Y \subset T$ is an irreducible component of $T$ :
 * $Y$ is irreducible
 * $Y$ is not a proper subset of an irreducible subspace of $T$.

That is, $Y$ is maximal in the ordered set of irreducible subspaces of $T$, ordered by the subset relation.

Also see

 * Point is Contained in Irreducible Component
 * Irreducible Component is Closed