Definition:Baire Space (Topology)/Definition 4

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

$T$ is a Baire space iff, whenever the union of any countable set of closed sets of $T$ has an interior point, then one of those closed sets must have an interior point.

Also see

 * Equivalence of Definitions of Baire Space