Particular Point Space is Non-Meager/Proof 2

Theorem

Let $T = \struct {S, \tau_p}$ be a particular point space.

Then $T$ is non-meager.

Proof

By definition of particular point space, any subset of $S$ which contains $p$ is open in $T$.

So $\left\{{p}\right\}$ itself is open in $T$.

That is, $p$ is an open point.

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

$\blacksquare$