Baire Space is Non-Meager

Theorem

Let $T = \struct {S, \tau}$ be a Baire space (in the context of topology).

Then $T$ is non-meager in $T$.

Proof

From Baire Space iff Open Sets are Non-Meager, all open sets of $T$ are non-meager in $T$.

But $T$ itself is an open set of $T$ by definition of topological space.

Hence the result.

$\blacksquare$