Either-Or Topology is Non-Meager/Proof 2

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Theorem

Let $T = \left({S, \tau}\right)$ 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.

$\blacksquare$