# Definition:Irreducible Component

## Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

A subspace $Y \subset T$ is an irreducible component of $T$ if and only if:

$Y$ is irreducible
$Y$ is not a proper subset of an irreducible subspace of $T$.

That is, if and only if $Y$ is maximal in the ordered set of irreducible subspaces of $T$, ordered by inclusion.