Arens-Fort Space is Completely Hausdorff

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Let $T = \struct {S, \tau}$ be the Arens-Fort space.

Then $T$ is a $T_{2 \frac 1 2}$ (completely Hausdorff) space.


We have:

Fort Space is Completely Normal
Arens-Fort Space is Expansion of Fort Space.

From Sequence of Implications of Separation Axioms we have that a Fort space is a $T_{2 \frac 1 2}$ space.

Then in Separation Properties Preserved by Expansion, it follows that as a Fort space is a $T_{2 \frac 1 2}$ space, then so is the Arens-Fort space.