Definition:Baire Space (Topology)/Definition 2

Definition

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

$T$ is a Baire space if and only if the intersection of any countable set of open sets of $T$ which are everywhere dense is everywhere dense.

Also see

• Equivalence of Definitions of Baire Space

• Results about Baire spaces can be found here.

Source of Name

This entry was named for René-Louis Baire.

Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Baire space