View source for Countably zero-dimensional space

A normal space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026750/c0267501.png" /> that can be represented in the form of a union <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026750/c0267502.png" /> of subspaces <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026750/c0267503.png" /> of dimension <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026750/c0267504.png" />.



====Comments====
If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026750/c0267505.png" /> 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.