Baire Space is Non-Meager
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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.
$\blacksquare$
Sources
- 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $22.1$: The Baire Category Theorem