Section Hausdorff_and_nets.
Require Export Nets.

Lemma net_limit_is_unique_cluster_point_impl_Hausdorff:
forall (X:TopologicalSpace),
(forall (I:DirectedSet) (x:Net I X) (x0 y:point_set X),
net_limit x x0 -> net_cluster_point x y ->
y = x0) -> Hausdorff X.