Order Topology is Normal

Theorem
Let $\left({S, \preceq}\right)$ be a toset.

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

Then $\left({S, \tau}\right)$ is normal.

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

The result follows from Completely Normal Space is Normal Space.