If a space has this property, then limits of nets and  lters on it are unique, and the intersection of all closed neighborhoods of x is equal to the   singleton {x}.
The original de nition of topological spaces included as an axiom that all spaces have this property, which a space has if it is both preregular and Kolmogorov. A space is said to be completely or functionally this if any two points in it can be separated by a continuous function. If a space has this property, then limits of nets and  lters on it are unique, and the intersection of all closed neighborhoods of x is equal to the   singleton {x}. This property's namesake also notably names a fractal dimension. For ten points, identify this property held by a topological space if any two distinct points in it have disjoint neighborhoods.
The original de nition of topological spaces included as an axiom that all spaces have this property, which a space has if it is both preregular and Kolmogorov.
Hausdorff  property [accept things like Hausdor  space, accept separatedness or T2 until  namesake  and prompt afterward]