Closure of Irreducible Subspace is Irreducible

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

Let $Y \subseteq S$ be a subset of $S$ which is irreducible in $T$.

Then its closure $Y^-$ in $T$ is also irreducible in $T$.

Also see

 * Closure of Connected Set is Connected