Baire Space iff Open Sets are Non-Meager

Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.

Then $T$ is a Baire space every non-empty open set of $T$ non-meager in $T$.

Historical Note
This result was the original definition which gave for the Baire space.

The more modern approach is to define it directly in terms of interiors of countable unions of closed sets.