In mathematics, a topological space is zero-dimensional if its topological dimension is zero, or equivalently, if it has a base consisting of clopen sets. A zero-dimensional Hausdorff space is necessarily totally disconnected, but the converse fails.

Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include Cantor space and Baire space.

Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers $2^I$ where 2={0,1} is given the discrete topology. Such a space is sometimes called a Cantor cube. If $I$ is countably infinite, $2^I$ is the Cantor space.

References

Dimension theory | Descriptive set theory | Properties of topological spaces

Przestrzeń zerowymiarowa | Нульмерное пространство