Ultraconnected Space is T4

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

Then $T$ is a $T_4$ space.

Proof
Recall the definition of a $T_4$ space:

$T = \struct {S, \tau}$ is a $T_4$ space :
 * for any two disjoint closed sets $A, B \subseteq S$, there exist disjoint open sets $U, V \in \tau$ containing $A$ and $B$ respectively.

As no two closed sets of an ultraconnected space are actually disjoint, it follows that $T_4$-ness follows vacuously.