A topological space T in which every two points *u*,*v*∈T have disjoint neighborhoods *u*∈U and *v*∈V separating them.

In a Hausdorff space, every point *u*∈T forms a closed set {*u*}.

Being Hausdorff is probably the single most important property a topological space can possess. So much so, it is often taken for granted.