# Countably zero-dimensional space

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 $\dim X_i\leq 0$.
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.