Arens-Fort Space is Paracompact/Proof 2

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

Then $T$ is a paracompact space.

Proof
We have that:
 * The Arens-Fort Space is Completely Normal.
 * The Arens-Fort Space is Lindelöf.

From Sequence of Implications of Separation Axioms, it follows that $T$ is a $T_3$ space.

The result follows from Lindelöf $T_3$ Space is Paracompact.