@@ -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,
13381337as 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]
13571356theorem 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
13621363If `β` is a normed `𝕜`-space, then we show that the space of bounded continuous
13631364functions from `α` to `β` is naturally a module over the algebra of bounded continuous
13641365functions from `α` to `𝕜`. -/
13651366
1366- variable {𝕜}
1367-
13681367instance 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 =>
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