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Countably zero-dimensional space

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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 $\dim X_i\leq 0$.


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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