Definition:Baire Space (Set Theory)
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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 Nicholas Moschovakis) $\NN$.
Source of Name
This entry was named for René-Louis Baire.