Require Export Nets.
Definition T0_sep (X:TopologicalSpace) : Prop :=
forall x y:point_set X, x <> y ->
(exists U:Ensemble (point_set X), open U /\ In U x /\ ~ In U y) \/
(exists U:Ensemble (point_set X), open U /\ ~ In U x /\ In U y).

Lemma topological_property_T0_sep : topological_property T0_sep.