High Quality Content by WIKIPEDIA articles! In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters. Intuitively, the condition is illustrated by the pun that a space is Hausdorff if any two points can be "housed off" from each other by open sets.