Arens-Fort Space is Non-Meager

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

Then $T$ is a second category space.

Proof
From First Category Sets in Arens-Fort Space, we have that $A \subseteq S$ is first category in $T$ iff $A = \left\{{\left({0, 0}\right)}\right\}$.

So as $\left\{{\left({0, 0}\right)}\right\} \ne S \subseteq S$, it follows that $T$ is a second category space.