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

Lemma quotient_projection_continuous {X : TopologicalSpace} (R : Relation (point_set X)) :
@continuous X (QuotientTopology R) (quotient_projection R).