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

Lemma quotient_projection_open_iff {X : TopologicalSpace} (R : Relation (point_set X))
(U : Ensemble (point_set (QuotientTopology R))) :
open (inverse_image (quotient_projection R) U) <-> open U.