diff --git a/theories/function_spaces.v b/theories/function_spaces.v index b7a516016..d1754a5d2 100644 --- a/theories/function_spaces.v +++ b/theories/function_spaces.v @@ -1555,61 +1555,6 @@ End cartesian_closed. End currying. -HB.mixin Record isContinuous {X Y : nbhsType} (f : X -> Y):= { - cts_fun : continuous f -}. - -#[short(type = "continuousType")] -HB.structure Definition Continuous {X Y : nbhsType} := { - f of @isContinuous X Y f -}. - -HB.instance Definition _ {X Y : topologicalType} := gen_eqMixin (continuousType X Y). -HB.instance Definition _ {X Y : topologicalType} := gen_choiceMixin (continuousType X Y). - -Lemma continuousEP {X Y : nbhsType} (f g : continuousType X Y) : - f = g <-> f =1 g. -Proof. -case: f g => [f [[ffun]]] [g [[gfun]]]/=; split=> [[->//]|/funext eqfg]. -rewrite eqfg in ffun *; congr {| Continuous.sort := _; Continuous.class := {| - Continuous.function_spaces_isContinuous_mixin := {|isContinuous.cts_fun := _|}|}|}. -exact: Prop_irrelevance. -Qed. - -Definition mkcts {X Y : nbhsType} (f : X -> Y) (f_cts : continuous f) := f. -HB.instance Definition _ {X Y : nbhsType} (f: X -> Y) (f_cts : continuous f) := - @isContinuous.Build X Y (mkcts f_cts) f_cts. - -Section continuous_comp. -Context {X Y Z : topologicalType}. -Context (f : continuousType X Y) (g : continuousType Y Z). - -Local Lemma cts_fun_comp : continuous (g \o f). -Proof. move=> x; apply: continuous_comp; exact: cts_fun. Qed. - -HB.instance Definition _ := @isContinuous.Build X Z (g \o f) cts_fun_comp. - -End continuous_comp. - -Section continuous_id. -Context {X : topologicalType}. - -Local Lemma cts_id : continuous (@idfun X). -Proof. by move=> ?. Qed. - -HB.instance Definition _ := @isContinuous.Build X X (@idfun X) cts_id. -End continuous_id. - -Section continuous_const. -Context {X Y : topologicalType} (y : Y). - -Local Lemma cts_const : continuous (@cst X Y y). -Proof. by move=> ?; exact: cvg_cst. Qed. - -HB.instance Definition _ := @isContinuous.Build X Y (cst y) cts_const. -End continuous_const. - - Lemma swap_continuous {X Y : topologicalType} : continuous (@swap X Y). Proof. case=> a b W /=[[U V]][] /= Ua Vb UVW; exists (V, U); first by split. @@ -3065,7 +3010,7 @@ Qed. End fundamental_groupoid_functor. End path_connected. - +(* HB.instance Definition _ {X : topologicalType} (A : set X) := Topological.copy (set_type A) (weak_topology set_val). @@ -3164,3 +3109,4 @@ Lemma van_kampen_simpleI : True ) . +*) \ No newline at end of file