helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma

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  14
  15 include "basic_topologies.ma".
  16 include "o-basic_topologies.ma".
  17 include "relations_to_o-algebra.ma".
  18
  19 definition o_basic_topology_of_basic_topology: basic_topology → Obasic_topology.
  20  intro;
  21  constructor 1;
  22   [ apply (POW' b);
  23   | apply (A b);
  24   | apply (J b);
  25   | apply (A_is_saturation b);
  26   | apply (J_is_reduction b);
  27   | apply (compatibility b); ]
  28 qed.
  29
  30 definition o_continuous_relation_of_continuous_relation:
  31  ∀BT1,BT2.continuous_relation BT1 BT2 →
  32   Ocontinuous_relation (o_basic_topology_of_basic_topology BT1) (o_basic_topology_of_basic_topology BT2).
  33  intros;
  34  constructor 1;
  35   [ apply (orelation_of_relation ?? c);
  36   | apply (reduced ?? c);
  37   | apply (saturated ?? c); ]
  38 qed.