# Countably zero-dimensional space

From Encyclopedia of Mathematics

A normal space $X$ that can be represented in the form of a union $X=\bigcup_{i=1}^{\infty}X_i$ of subspaces $X_i$ of dimension $\dim X_i\leq 0$.

#### Comments

If $X$ is a metrizable space, then its countable zero-dimensionality is equivalent to it being countable dimensional, i.e. being the union of countably many finite-dimensional subspaces.

**How to Cite This Entry:**

Countably zero-dimensional space.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Countably_zero-dimensional_space&oldid=39009

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article