Editing Zero-dimensional space (section)

== Definition ==
Specifically:
* A topological space is zero-dimensional with respect to the [[Lebesgue covering dimension]] if every [[open cover]] of the space has a [[refinement (topology)|refinement]] that is a cover by disjoint open sets.
* A topological space is zero-dimensional with respect to the finite-to-finite covering dimension if every finite open cover of the space has a refinement that is a finite open cover such that any point in the space is contained in exactly one open set of this refinement.
* A topological space is zero-dimensional with respect to the [[small inductive dimension]] if it has a [[base (topology)|base]] consisting of [[clopen set]]s.
The three notions above agree for [[Separable space|separable]], [[metrisable space]]s.{{citation needed|reason=Please cite a proof.|date=April 2017}}{{clarify|reason=Is the agreement only for the zero dimensional-case, or for all dimensions?|date=April 2017}}