Discrete Space is Non-Meager/Proof 2

Theorem

Let $T = \struct {S, \tau}$ 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 $\set x$ is open in $T$.

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

$\blacksquare$