# Baire Space is Non-Meager

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## Theorem

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

$\blacksquare$