Zero-dimensional space

In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. A graphical illustration of a nildimensional space is a point.
Definition.
Specifically:
The three notions above agree for separable, metrisable spaces.
Hypersphere.
The zero-dimensional hypersphere is a pair of points. The zero-dimensional ball is a point.