Namespaces
Variants
Actions

Baire space

From Encyclopedia of Mathematics
Revision as of 12:13, 8 February 2012 by Ottos mops (talk | contribs) (TeX)
Jump to: navigation, search

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=20899
This article was adapted from an original article by P.S. Aleksandrov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article