Topological Closure of Singleton is Irreducible

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

Let $x$ be a point of $T$.

Then:
 * $\left\{ {x}\right\}^-$ is irreducible

where $\left\{ {x}\right\}^-$ denotes the topological closure of $\left\{ {x}\right\}$.