# Baire space

From Encyclopedia of Mathematics

Any space in which the Baire theorem on complete spaces is valid.

The metric space the points of which are infinite sequences of natural numbers, and the distance is given by the formula:

where is the first natural number for which . This is a complete metric separable zero-dimensional space containing the topological image of any metric separable zero-dimensional space.

**How to Cite This Entry:**

Baire space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Baire_space&oldid=18092

This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article