Definition:Baire Space (Set Theory)

Definition
The Baire space 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.

It can be denoted $\mathbf B$, $\N^\N$ or (as used by Yiannis Moschovakis) $\mathcal N$.