A zero-dimensional space with respect to the small inductive dimension has a base consisting of clopen sets.

The almost discrete spaces are precisely the finitely generated zero-dimensional spaces.

AE(0), an absolute extensor for compact zero-dimensional spaces.

Apart from the trivial case of a zero-dimensional space over any field, a vector space over a field F has a finite number of elements if and only if F is a finite field and the vector space has a finite dimension.