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).
Definition T1_sep (X:TopologicalSpace) : Prop :=
forall x:point_set X, closed (Singleton x).

Lemma topological_property_T1_sep : topological_property T1_sep.