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.
The three notions above agree for separable, metrisable spaces.[clarification needed]
All points of a zero-dimensional manifold are isolated.
In particular, the zero-dimensional hypersphere is a pair of points, and the zero-dimensional ball is a single point.