Arens-Fort Space is Completely Normal

Theorem
Let $T = \left({S, \tau}\right)$ be the Arens-Fort space.

Then $T$ is a completely normal space.

Consequently, $T$ satisfies all weaker separation axioms.

Proof
We have:
 * Arens-Fort Space is $T_1$
 * Arens-Fort Space is $T_5$

and so by definition $T$ is completely normal.

See Sequence of Implications of Separation Axioms for confirmation of the statement about weaker separation axioms.