Section Hausdorff_and_nets.

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