Require Export TopologicalSpaces.
Definition QuotientTopology {X : TopologicalSpace} (R : Relation (point_set X)) :
TopologicalSpace := StrongTopology (True_rect (quotient_projection R)).

Lemma quotient_separable {X : TopologicalSpace} (R : Relation (point_set X)) :
separable X -> separable (QuotientTopology R).