Discrete Space is Non-Meager/Proof 2

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Theorem

Let $T = \left({S, \tau}\right)$ be a discrete topological space.

Then $T$ is non-meager.


Proof

Let $x \in S$ be an arbitrary point of $T$.

From Set in Discrete Topology is Clopen it follows that $\left\{{x}\right\}$ is open in $T$.

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

$\blacksquare$