Either-Or Topology is Non-Meager/Proof 2

Theorem

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

Then $T$ is non-meager.

Proof

From the definition of the either-or space, we have that every point $x$ in $T$ (apart from $0$) forms an open set of $T$.

The result follows directly from Space with Open Point is Non-Meager.

$\blacksquare$