# Definition:Baire Space (Set Theory)

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## 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 Nicholas Moschovakis) $\NN$.

## Source of Name

This entry was named for RenĂ©-Louis Baire.