Difference between revisions of "Countably zero-dimensional space"
From Encyclopedia of Mathematics
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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. | ||
Latest revision as of 11:16, 5 July 2016
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://encyclopediaofmath.org/index.php?title=Countably_zero-dimensional_space&oldid=17731
Countably zero-dimensional space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Countably_zero-dimensional_space&oldid=17731
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article