Strong zero-dimensionality
= Strong zero-dimensionality
In a normal Hausdorff space, strong zero-dimensionality means that any disjoint closed sets can be separated by a <clopen set>, equivalently by disjoint clopen neighborhoods. For general <Tychonoff spaces>, the usual definition asks this for completely separated sets. In the normal setting <Urysohn's lemma> makes the formulations agree. The condition is equivalent to zero-dimensionality of the <Stone-Čech compactification>.