Ultraconnected Space is not necessarily Arc-Connected

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

Then $T$ is not necessarily arc-connected.

Proof
Let $T$ be an excluded point space.

From Excluded Point Space is Ultraconnected, $T$ is an ultraconnected space.

From Excluded Point Space is not Arc-Connected, $T$ is not arc-connected.

Hence the result.