diff --git a/_CoqProject b/_CoqProject index b7a78865c..7a09f3f43 100644 --- a/_CoqProject +++ b/_CoqProject @@ -28,7 +28,7 @@ theories/topology.v theories/function_spaces.v theories/cantor.v theories/prodnormedzmodule.v -theories/evt.v +theories/tvs.v theories/normedtype.v theories/realfun.v theories/sequences.v diff --git a/theories/Make b/theories/Make index a0f868e85..5243f4661 100644 --- a/theories/Make +++ b/theories/Make @@ -16,7 +16,7 @@ topology.v function_spaces.v cantor.v prodnormedzmodule.v -evt.v +tvs.v normedtype.v realfun.v sequences.v diff --git a/theories/normedtype.v b/theories/normedtype.v index 1bebfc9ac..026b33158 100644 --- a/theories/normedtype.v +++ b/theories/normedtype.v @@ -6,7 +6,7 @@ From mathcomp Require Import boolp classical_sets functions. From mathcomp Require Import archimedean. From mathcomp Require Import cardinality set_interval Rstruct. Require Import ereal reals signed topology prodnormedzmodule function_spaces. -Require Import evt. +Require Import tvs. (**md**************************************************************************) (* # Norm-related Notions *) @@ -791,6 +791,11 @@ HB.mixin Record PseudoMetricNormedZmod_Lmodule_isNormedModule K V normrZ : forall (l : K) (x : V), `| l *: x | = `| l | * `| x |; }. +(*#[short(type="normedModType")] +HB.structure Definition NormedModule (K : numDomainType) := + {T of TopologicalLmodule K T & GRing.Lmodule K T + & PseudoMetricNormedZmod_Lmodule_isNormedModule K T}.*) + #[short(type="normedModType")] HB.structure Definition NormedModule (K : numDomainType) := {T of PseudoMetricNormedZmod K T & GRing.Lmodule K T @@ -805,6 +810,22 @@ HB.instance Definition _ := NormedZmod_PseudoMetric_eq.Build R R^o erefl. HB.instance Definition _ := PseudoMetricNormedZmod_Lmodule_isNormedModule.Build R R^o (@normrM _). +(*Let Ro_add_continuous : continuous (uncurry (@GRing.add R^o)). +Proof. +Admitted. + +Let Ro_scale_continuous : + continuous (uncurry (@GRing.scale R R^o) : R^o * R^o -> R^o). +Admitted. + +Let Ro_locally_convex : exists2 B : set (set R^o), + (forall b, b \in B -> convex b) & basis B. +Admitted. + +HB.instance Definition _ := + TopologicalLmod_isTvs.Build R R^o Ro_add_continuous + Ro_scale_continuous Ro_locally_convex.*) + End regular_topology. Lemma ball_itv {R : realFieldType} (x r : R) : diff --git a/theories/evt.v b/theories/tvs.v similarity index 94% rename from theories/evt.v rename to theories/tvs.v index 98c421438..f58bcb865 100644 --- a/theories/evt.v +++ b/theories/tvs.v @@ -18,8 +18,8 @@ Local Open Scope ring_scope. HB.structure Definition PointedNmodule := {M of Pointed M & GRing.Nmodule M}. HB.structure Definition PointedZmodule := {M of Pointed M & GRing.Zmodule M}. -HB.structure Definition PointedLmodule (K : numDomainType) := - {M of Pointed M & GRing.Lmodule K M}. +HB.structure Definition PointedLmodule (K : numDomainType) := {M of Pointed M & GRing.Lmodule K M}. + HB.structure Definition FilteredNmodule := {M of Filtered M M & GRing.Nmodule M}. HB.structure Definition FilteredZmodule := {M of Filtered M M & GRing.Zmodule M}. HB.structure Definition FilteredLmodule (K : numDomainType) := @@ -28,7 +28,8 @@ HB.structure Definition NbhsNmodule := {M of Nbhs M & GRing.Nmodule M}. HB.structure Definition NbhsZmodule := {M of Nbhs M & GRing.Zmodule M}. HB.structure Definition NbhsLmodule (K : numDomainType) := {M of Nbhs M & GRing.Lmodule K M}. -HB.structure Definition TopologicalNmodule := {M of Topological M & GRing.Nmodule M}. + +(*HB.structure Definition TopologicalNmodule := {M of Topological M & GRing.Nmodule M}.*) HB.structure Definition TopologicalZmodule := {M of Topological M & GRing.Zmodule M}. HB.structure Definition TopologicalLmodule (K : numDomainType) := @@ -40,7 +41,7 @@ HB.structure Definition UniformLmodule (K : numDomainType) := Definition convex (R : ringType) (M : lmodType R) (A : set M) := forall x y lambda, lambda *: x + (1 - lambda) *: y \in A. -HB.mixin Record Uniform_isEvt (R : numDomainType) E of Uniform E & GRing.Lmodule R E := { +HB.mixin Record Uniform_isTvs (R : numDomainType) E of Uniform E & GRing.Lmodule R E := { add_continuous : continuous (fun x : E * E => x.1 + x.2) ; (*continuous (uncurry (@GRing.add E))*) scale_continuous : continuous (fun z : R^o * E => z.1 *: z.2) ; @@ -49,17 +50,17 @@ HB.mixin Record Uniform_isEvt (R : numDomainType) E of Uniform E & GRing.Lmodule }. #[short(type="evtType")] -HB.structure Definition Evt (R : numDomainType) := - {E of Uniform_isEvt R E & Uniform E & GRing.Lmodule R E}. +HB.structure Definition Tvs (R : numDomainType) := + {E of Uniform_isTvs R E & Uniform E & GRing.Lmodule R E}. -HB.factory Record TopologicalLmod_isEvt (R : numFieldType) E +HB.factory Record TopologicalLmod_isTvs (R : numFieldType) E of Topological E & GRing.Lmodule R E := { add_continuous : continuous (uncurry (@GRing.add E)); scale_continuous : continuous (uncurry (@GRing.scale R E) : R^o * E -> E); locally_convex : exists2 B : set (set E), (forall b, b \in B -> convex b) & basis B }. -HB.builders Context R E of TopologicalLmod_isEvt R E. +HB.builders Context R E of TopologicalLmod_isTvs R E. Definition entourage : set_system (E * E):= fun P => exists U, nbhs 0 U /\ (forall xy : E * E, (xy.1 - xy.2) \in U -> xy \in P).