Particular Point Space is Non-Meager/Proof 2

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Theorem

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

$\blacksquare$