-(* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
-definition o_basic_topology_of_basic_topology: cic:/matita/formal_topology/basic_topologies/basic_topology.ind#xpointer(1/1) → basic_topology.
- intro;
+definition o_basic_topology_of_basic_topology: basic_topology → Obasic_topology.
+ intros (b); constructor 1;
+ [ apply (POW' b) | apply (A b) | apply (J b);
+ | apply (A_is_saturation b) | apply (J_is_reduction b) | apply (compatibility b) ]
+qed.
+
+definition o_continuous_relation_of_continuous_relation:
+ ∀BT1,BT2.continuous_relation BT1 BT2 →
+ Ocontinuous_relation (o_basic_topology_of_basic_topology BT1) (o_basic_topology_of_basic_topology BT2).
+ intros (BT1 BT2 c); constructor 1;
+ [ apply (orelation_of_relation ?? c) | apply (reduced ?? c) | apply (saturated ?? c) ]
+qed.
+
+axiom daemon: False.
+
+lemma o_continuous_relation_of_continuous_relation_morphism :
+ ∀S,T:category2_of_category1 BTop.
+ unary_morphism2 (arrows2 (category2_of_category1 BTop) S T)
+ (arrows2 OBTop (o_basic_topology_of_basic_topology S) (o_basic_topology_of_basic_topology T)).
+intros (S T);
+ constructor 1;
+ [ apply (o_continuous_relation_of_continuous_relation S T);
+ | cases daemon (*apply (o_relation_pair_of_relation_pair_is_morphism S T)*)]
+qed.
+
+definition BTop_to_OBTop: carr3 (arrows3 CAT2 (category2_of_category1 BTop) OBTop).