\begin{definition}[Definition:Irreducible Component]
Let $T = \left({S, \tau}\right)$ be a topological space.
A subspace $Y \subset T$ is an '''irreducible component of $T$''' {{iff}}:
: $Y$ is irreducible
: $Y$ is not a proper subset of an irreducible subspace of $T$.
That is, {{iff}} $Y$ is maximal in the ordered set of irreducible subspaces of $T$, ordered by inclusion.
\end{definition}