Skip to content

Commit 210c7a1

Browse files
committed
minor changes
1 parent 980fa3f commit 210c7a1

1 file changed

Lines changed: 6 additions & 7 deletions

File tree

Mathlib/Topology/ContinuousMap/Bounded/Basic.lean

Lines changed: 6 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -650,8 +650,7 @@ instance instMulOneClass [MulOneClass R] [BoundedMul R] [ContinuousMul R] : MulO
650650
@[to_additive (attr := simps)
651651
"Composition on the left by a (lipschitz-continuous) homomorphism of topological `AddMonoid`s, as a
652652
`AddMonoidHom`. Similar to `AddMonoidHom.compLeftContinuous`."]
653-
protected def _root_.MonoidHom.compLeftContinuousBounded (α : Type*) {β : Type*} {γ : Type*}
654-
[TopologicalSpace α]
653+
protected def _root_.MonoidHom.compLeftContinuousBounded (α : Type*) [TopologicalSpace α]
655654
[PseudoMetricSpace β] [Monoid β] [BoundedMul β] [ContinuousMul β]
656655
[PseudoMetricSpace γ] [Monoid γ] [BoundedMul γ] [ContinuousMul γ]
657656
(g : β →* γ) {C : NNReal} (hg : LipschitzWith C g) :
@@ -1239,9 +1238,9 @@ instance instSeminormedRing : SeminormedRing (α →ᵇ R) where
12391238
__ := instNonUnitalSeminormedRing
12401239

12411240
/-- Composition on the left by a (lipschitz-continuous) homomorphism of topological semirings, as a
1242-
`RingHom`. Similar to `RingHom.compLeftContinuous`. -/
1241+
`RingHom`. Similar to `RingHom.compLeftContinuous`. -/
12431242
@[simps!]
1244-
protected def _root_.RingHom.compLeftContinuousBounded (α : Type*) {β : Type*} {γ : Type*}
1243+
protected def _root_.RingHom.compLeftContinuousBounded (α : Type*)
12451244
[TopologicalSpace α] [SeminormedRing β] [SeminormedRing γ]
12461245
(g : β →+* γ) {C : NNReal} (hg : LipschitzWith C g) : (α →ᵇ β) →+* (α →ᵇ γ) :=
12471246
{ g.toMonoidHom.compLeftContinuousBounded α hg,
@@ -1337,7 +1336,7 @@ variable (𝕜)
13371336
/-- Composition on the left by a (lipschitz-continuous) homomorphism of topological `R`-algebras,
13381337
as an `AlgHom`. Similar to `AlgHom.compLeftContinuous`. -/
13391338
@[simps!]
1340-
protected def AlgHom.compLeftContinuousBounded {α : Type*} [TopologicalSpace α]
1339+
protected def AlgHom.compLeftContinuousBounded
13411340
[NormedRing β] [NormedAlgebra 𝕜 β][NormedRing γ] [NormedAlgebra 𝕜 γ]
13421341
(g : β →ₐ[𝕜] γ) {C : NNReal} (hg : LipschitzWith C g) : (α →ᵇ β) →ₐ[𝕜] (α →ᵇ γ) :=
13431342
{ g.toRingHom.compLeftContinuousBounded α hg with
@@ -1356,15 +1355,15 @@ def toContinuousMapₐ : (α →ᵇ γ) →ₐ[𝕜] C(α, γ) where
13561355
@[simp]
13571356
theorem coe_toContinuousMapₐ (f : α →ᵇ γ) : (f.toContinuousMapₐ 𝕜 : α → γ) = f := rfl
13581357

1358+
variable {𝕜}
1359+
13591360
/-!
13601361
### Structure as normed module over scalar functions
13611362
13621363
If `β` is a normed `𝕜`-space, then we show that the space of bounded continuous
13631364
functions from `α` to `β` is naturally a module over the algebra of bounded continuous
13641365
functions from `α` to `𝕜`. -/
13651366

1366-
variable {𝕜}
1367-
13681367
instance instSMul' : SMul (α →ᵇ 𝕜) (α →ᵇ β) where
13691368
smul f g :=
13701369
ofNormedAddCommGroup (fun x => f x • g x) (f.continuous.smul g.continuous) (‖f‖ * ‖g‖) fun x =>

0 commit comments

Comments
 (0)