Definition:Baire Property

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a subset of $S$.

Then $H$ has the Baire property if and only if there exists an open set $U \in \tau$ such that the symmetric difference $U \symdif H$ is meager.

Also see

• Results about the Baire property can be found here.

Source of Name

This entry was named for René-Louis Baire.

Sources

• 1973: Thomas J. Jech: The Axiom of Choice ... (previous) ... (next): $1.$ Introduction: $1.4$ Problems