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Baire space

From Encyclopedia of Mathematics
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Any space in which the Baire theorem on complete spaces is valid.

The metric space the points of which are infinite sequences $\{n_i\}=\{n_1,n_2,\dotsc\}$ of natural numbers, and the distance is given by the formula:

$$\rho(\{n_i\},\{m_i\}) = \frac1{k_0}$$

where $k_0$ is the first natural number $k$ for which $n_k\neq m_k$. 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=20898
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article