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.

$\blacksquare$