Require Export Nets.

Lemma metric_space_net_cluster_point_converse: forall (X:TopologicalSpace)
(d:point_set X -> point_set X -> R), metrizes X d ->
forall (I:DirectedSet) (x:Net I X) (x0:point_set X),
net_cluster_point x x0 -> forall eps:R, eps > 0 ->
exists arbitrarily large i:DS_set I, d x0 (x i) < eps.