Baire Space iff Open Sets are Second Category
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Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.
Then $T$ is a Baire space iff every non-empty open set of $T$ is of the second category in $T$.
Proof
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Comment
This result was the original definition which Baire gave for the Baire space.
The more modern approach is to define it directly in terms of interiors of countable unions of closed sets.
