include "o-basic_topologies.ma".
include "relations_to_o-algebra.ma".
-(* 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.
+definition o_basic_topology_of_basic_topology: basic_topology → Obasic_topology.
intro;
constructor 1;
- [ apply (SUBSETS (carrbt b));
+ [ apply (POW' b);
| apply (A b);
| apply (J b);
| apply (A_is_saturation b);
| apply (compatibility b); ]
qed.
-definition o_relation_pair_of_relation_pair:
- ∀S,T.cic:/matita/formal_topology/basic_topologies/continuous_relation.ind#xpointer(1/1) S T →
- continuous_relation (o_basic_topology_of_basic_topology S) (o_basic_topology_of_basic_topology T).
+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;
constructor 1;
- [ apply (orelation_of_relation ?? (cont_rel ?? c));
+ [ apply (orelation_of_relation ?? c);
| apply (reduced ?? c);
| apply (saturated ?? c); ]
qed.
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