Irreducible Components of Hausdorff Space are Points

Theorem
Let $X$ be a Hausdorff space.

Then the irreducible components of $X$ are the singleton sets.

Proof
By Subspace of Hausdorff Space is Hausdorff, the irreducible components of $X$ are also Hausdorff.

By Irreducible Hausdorff Space is Singleton, they can only be singletons.

By Trivial Topological Space is Irreducible, every singleton of $X$ is indeed irreducible.