Definition:Baire Space (Set Theory)

Definition
The Baire space $\mathbf B$ is defined as the set of all infinite sequences of natural numbers.

It can also be defined as the Cartesian product of a countably infinite number of copies of the set of natural numbers.

Also denoted as
The Baire space $\mathbf B$ can also be denoted $\N^\N$ or (as used by Yiannis Moschovakis) $\mathcal N$.