Order Topology is Normal

Theorem
Let $\struct {S, \preceq}$ be a toset.

Let $\tau$ be the order topology on $S$.

Then $\struct {S, \tau}$ is normal.

Proof
From Linearly Ordered Space is Completely Normal, $\struct {S, \tau}$ is a completely normal space.

The result follows from Completely Normal Space is Normal Space.